We study time-periodic Taylor-Couette flow with the outer cylinder at rest and the inner one oscillating with a mean angular velocity. Varying the frequency of inner cylinder, we investigate the change of Taylor vortices at a given amplitude and a mean angular velocity. With a small frequency of modulation, we find that Taylor vortices appear and disappear periodically. With a higher frequency, Taylor vortices do not disappear, but the intensity of Taylor vortices modulates periodically. As the frequency increases, Taylor vortices modulate harmonically.