The large-scale grid connection of renewable energy represented by wind power threatens the safe and stable operation of electric system. The vigorous development pumped storage power station (PSPS) is a global consensus to support the grid-connected of renewable energy. This paper investigates the transient behavior of pumped storage-wind (PSW) hybrid power system under grid-connected operation condition (GCOC). Firstly, a model of PSW hybrid power system under GCOC is constructed. The stable domain is determined according to Hopf bifurcation theory. The influence of system parameters on the stability of PSW hybrid power system under GCOC is analyzed. A synergetic control strategy is designed to improve the dynamic performance of the system. Then, the mechanism of multi-time-scale dynamic response is revealed. Finally, the transient behavior of PSPS under different application scenarios and the interaction between PSPS and wind power station (WPS) are studied. The results show that the stability of PSW hybrid power system under GCOC can be judged by stable domain. The designed synergetic control strategy can improve the dynamic performance of the system. The dynamic response is composed of three oscillations with different frequencies, namely, mass oscillation at low frequency, water hammer oscillation at medium frequency, and electrical oscillation at high frequency. The principal oscillation is caused by water hammer. The interaction between PSPS and WPS has a significant effect on the transient behavior. By adjusting the interaction between PSPS and WPS, the system can absorb more wind power while ensuring safe and stable operation, which can increase profits and avoid unnecessary operation oscillations. The analytical methods and results presented in this paper are of great significance for improving the ability of power grid to accept renewable energy.