Shaken students stood outside the building waiting for news
Students' reaction
Mayor Frank Jackson said four people were wounded when the teenager entered the SuccessTech Academy and walked down a corridor on the fourth floor firing.
Two teenage boys and two adults were shot, and another girl injured her knee while fleeing, Mr Jackson said.
Local media reported the attacker had been unhappy at having been suspended.
The SuccessTech Academy is a 250-student alternative high school that specialises in business and technology.
It is based on several floors of the Lakeside Avenue administration building in the city centre.
'Gun in each hand'
At a news conference, Cleveland Police Chief Michael McGrath said his force's initial investigation indicated that the 14-year-old boy had killed himself before police arrived and that he had at least two guns.
When he got suspended, he said 'I got something for y'all'
SuccessTech Academy student
Timeline: US school shootings
Mr McGrath said video surveillance would allow them to determine how long the gunman was in the school before the shooting, but the student is believed to have arrived early on Wednesday morning.
The main scene of the shooting on the 4th floor of the Lakeside Avenue building is still being processed by the city's coroner's office, he added.
Witnesses reported having seen the shooter roam through school corridors with a gun in each hand.
Ronnell Jackson, 15, told the Associated Press that he saw the attacker running down a hallway.
The victims of the shooting are in a stable condition in hospital
"He was aiming at me, I got out just in time," he said.
Some students and staff fled after hearing shots and an alert on the school public address system. Others attempted to hide in cupboards or under desks.
Afterwards, shaken students and worried relatives stood outside the building waiting for news.
One student told Philadelphia Channel 6 Action News that the student was a goth and had been wearing a trenchcoat, boots and a chain.
"When he got suspended, he said 'I got something for y'all'," she added.
Schools closed
Cleveland's mayor said those injured in the shooting included two teenage boys aged 14 and 17, who were both in a "stable, good condition".
Schools are supposed to be safe places
Joanne DeMarco
Cleveland Teachers' Union
A 57-year-old man and a 42-year-old man were hurt slightly more seriously and are in "a little elevated condition", Mayor Jackson said.
"The families of all of the victims have been notified, and we are currently connecting all the children and parents with people who can help them through this," he added.
The chief executive of the Cleveland Municipal School District, Eugene Sanders, announced that all the school's activities had been cancelled until Monday.
All public schools in Cleveland will be closed on Thursday, he said, so that students and teachers can "take a breather" and "put this in perspective".
Shock
Joanne DeMarco, president of the Cleveland Teachers' Union, said she was surprised at the shooting.
"Schools are supposed to be safe places, safe places. And you know, it's not that Cleveland's immune to anything that's going on in the nation, but SuccessTech would have been the last place we would have thought of," she said.
Responding to reports that a teenage student may have been responsible, a reader from Cleveland told the BBC News website that the school had been getting good results.
"It's a shame one kid has spoiled all that... and an even bigger shame that due to budget cuts the security the school needed wasn't in place," she said.
Several parents have complained in interviews with local media that the school had recently denied requests to hire a security guard.
The incident comes six months after the US suffered its worst ever campus shooting, when a gunman killed more than 30 students and staff at Virginia Tech.
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Location of Ohio within the United States.
A 14-year-old student opened fire in a Cleveland, Ohio high school today, wounding four people. The gunman then fatally shot himself.

Police were called to the scene at 1:15 p.m. EST, with reports of a gunman in the school. The gunman, 14-year-old Asa H. Coon, entered the school with a gun in each hand. Students were evacuated, with the gunman reportedly still in the building for some time afterward.

According to Cleveland mayor Frank Jackson, two adult males, ages 57 and 42, and two teenage males, ages 18 and 14, were wounded, and taken to local hospitals. A third teenager, a 14-year-old female, hurt her knee while running from the school.

A spokesperson for the hospital would not give details of the students' names or conditions, but Jackson said in an afternoon press conference that all three teenagers were in stable condition.

According to one student, 14-year-old student Michael Peek was the first person shot, after reportedly punching Coon in the face.  The student indicated that Peek did not know that Coon was armed at the time. 18-year-old student Darnell Rodgers told the media that he was the other student shot, a graze wound for which he was treated and subsequently released.

The 57-year-old teacher, David Kachadourian, was listed in good condition. 42-year-old teacher Michael Grassie was in surgery and his condition was unavailable.

The gunman was reportedly upset about a recent suspension arising from a fight that happened Monday near the school.

According to one student interviewed by ''CNN'', the gunman said he "worshiped the devil" and had mentioned committing a shooting at the school. Another student noted that the gunman often wore a trench coat and an empty pistol belt to class.

A security guard was present on the first floor of the building, but the position of a guard on the third floor was eliminated. While metal detectors were present in the building, they were not always in use; it is unclear whether they were in use at the time of the shooting.

The school, SuccessTech Academy, is a non-traditional school within the Cleveland Metropolitan School District, described on their web site as a "small, nontraditional high school that provides a learning environment in which all student believe in their ability to succeed."  It opened five years ago.

SuccessTech is located on the third, fourth and fifth floors of a building in downtown Cleveland that also houses some administrative offices.

The school owes its existence in part to a grant from the Bill and Melinda Gates Foundation, which helped to fund the creation of the school.