  We study the chiral phase transition of quark matter under rotation in
two-flavor Nambu--Jona-Lasinio (NJL) model. It is found that, in the rotating
frame, the angular velocity plays the similar role as the baryon chemical
potential and suppresses the chiral condensate, thus the chiral phase
transition shows a critical end point not only in the temperature-chemical
potential $T-\mu$ plane, but also in the temperature-angular momentum
$T-\omega$ plane. One interesting observation is that in the $T-\mu$ plane, the
presence of the angular momentum only shifts down the critical temperature
$T^E$ of the CEP and does not shift the critical chemical potential $\mu^E$,
and in the $T-\omega$ plane, the increase of the chemical potential only shift
down the critical temperature $T^E$ and does not change the critical angular
momentum $\omega^E$. The phase structure in the $T-\mu$ plane is sensitive to
the coupling strength in the vector channel, while the phase structure in
$T-\omega$ plane is not. It is also observed that the rotating angular velocity
suppresses the kurtosis of the baryon number fluctuations, while it enhances
the pressure density, energy density, the specific heat and the sound velocity.
