Aiming at two cylinders which is a very typical multi-cylinder structure, the influence of staggered distances on the flow-induced vibration response characteristics of two circular cylinders is studied using numerical simulation method. and the interaction relation between the gap flow and the vibration response of cylinders is obtained. The results illustrate that FIM mode of two cylinders include periodic vibration, double-cycle vibration, multiple-periodic vibration, and quasi-periodic vibration. With the change of staggered spacing, the amplitude of upstream cylinder is almost unaffected, and maximizes at U^*=6. For the downstream cylinder, the change of staggered distance will significantly affect the trend of amplitude curve, especially when T=0.6D (D is the diameter of the cylinder). With the change of inflow velocity, the amplitude curves of upstream and downstream cylinders intersect, and there is a critical reduced-velocity U_c^*=7. When U^* > U_c^*, the amplitude of upstream cylinder is lower than that of downstream cylinder. It is the dominant region of gap flow for T>0.6D and U^* <8. In this region, vortices shed from the upstream cylinder form a gap flow, which attaches to the surface of the downstream cylinder, leading to the advance of boundary layer separation of the downstream cylinder, and enhancing the vibration of the cylinder.