The vortex-induced vibration (VIV) of a cylinder with mass ratio 2.6 and damping ratio 0.0036 at different reduced velocities has been numerically simulated based on the overset grid method. The amplitude, frequency ratio, wake vortex shedding modes and nonlinear characteristics of the VIV response are systematically analyzed. With the increase of the reduced velocity, the VIV response of the cylinder switches four times, but only once the phase difference between the transverse flow vibration response and the vortex force coefficient changes abruptly, which causes the wake vortex shedding mode to change from “2T” mode to “2P” mode. In addition, the velocity variation range of the VIV of the cylinder is smaller than its displacement variation range under any reduced velocities. When the reduced velocity is 4.0, the VIV of the cylinder is chaotic in both the streamwise and transverse directions. When the reduced velocity is 8.0, the VIV of the cylinder is also chaotic in the transverse direction, but still is self-limited. Under the other reduced velocities, the vibrations of the cylinder are regular and stable in the streamwise and transverse directions.