The finite-difference time-domain (FDTD) method is developed for analyzing the photonic crystals in the non-inertial frame. The difference equations and the perfectly matched layer absorbing boundary condition equations in the non-inertial frame are given. Designing a photonic crystal structure with a ring cavity and a directional coupler. The length of directional coupler is 43a, which keep the high quality factor and necessary frequency resolution. The theoretical results indicate that there is frequency tolerance between wave propagating along the clockwise and counter-clockwise in the ring cavity. The frequency tolerance depends on the rotational speed.