  A conventional space-time diagram is $r-ct$ one, which satisfies the
Minkowski geometry. This geometry conflict the intuition from the Euclid
geometry. In this work an Euclid space-time diagram is proposed to describe
relativistic world lines with an exact Euclid geometry. The relativistic
effects such as the dilation of moving clocks, the contraction of moving
length, and the twin paradox can be geometrically expressed in the Euclid
space-time diagram. It is applied to the case of a satellite clock to correct
the gravitational effect. It is found that this Euclid space-time diagram is
much more intuitive than the conventional space-time diagram.
