In order to clarify the effect of the motion of the upstream cylinder on the vortex-induced vibration of the downstream cylinder，two different cases，namely whether the upstream cylinder is fixed or not，are taken into consideration. Numerical simulation is employed to investigate the vortex-induced vibration of the downstream cylinder at Re=100. The vibration characteristics，including amplitudes，vibration frequencies and phase lags between two cylinders，are discussed with the variation of reduced velocity. The wake flow structures and energy input mechanisms of the vortex-induced vibration are explored. Results show that the vibrating condition of the upstream cylinder imposes a significant influence on the vortex-induced vibration of the downstream cylinder. Compared with the condition of a fixed upstream cylinder，an obvious lock-in phenomenon is observed when the upstream cylinder can vibrate in two-degree-of-freedom and the downstream cylinder is subjected to a larger transverse amplitude and the maximum amplitude occurs at higher reduced velocity. In addition，the flow structures around two cylinders are different in the two cases when the downstream cylinder undergoes maximum amplitude. Parallel vortex street mode is observed when the upstream cylinder is fixed，whereas‘2S’wake mode is inspected when the upstream cylinder is allowed to vibrate.