  We study the entanglement entropy between a strip region with width $2R$ and
its complement in strongly coupled large-$N$ conformal field theory (CFT) on
$\mathbb{R}^{1,n}$ with chemical potential and angular momentum in an thermal
equilibrium state, which dual to the cylindrical Kerr-Newman black hole. Using
Ryu-Takanayagi conjecture, we are able to explore the entanglement entropy
through calculating the area of the extremal surface which is anchored on the
entangled surface. Because we consider the rotating charged black hole for the
gravitational dual, the entropy can be characterized by the mass $m$, charge
$q$ and rotation $a$ parameters. We find that in the small $R$ limit, only the
mass $m$ and the rotation $a$ parameters come in the leading behavior, the
quadratic of $R$ term, after subtracting the entanglement entropy in vacuum. In
the large $R$ limit, the area of the extremal surface is very close to the area
of the event horizon after regularization. When we take the whole spatial
region, the entanglement entropy is identical to the thermal entropy, i.e. the
Bekenstein-Hawking entropy.
