Four large hydropower stations have recently been built downstream the Jinsha River in Southwestern China with a strong regional tectonic activity background. There is widely felt seismicity since the impoundment of the Xiluodu and Xiangjiaba reservoirs, increasing the public concern in this region. We begin with a criticality analysis of the faults near these reservoirs to quantify their susceptibility to triggered seismicity. Then we focus on the Xiluodu reservoir to investigate the correlation between the impoundment and seismicity nearby. We analyze the spatio-temporal distribution of seismicity near the Xiluodu reservoir, and identify the plausible rapid and delayed seismic response due to the impoundment. According to the impoundment record, we explicitly model the hydro-mechanical changes due to diffusion and reservoir water load, i.e., in pore pressure, elastic stress, and the resulting Coulomb stress. Our results show that the pore pressure changes can reach a level that may trigger fault reactivation and consequently, seismicity nearby. The water load can also induce the positive Coulomb stress changes on faults, depending on the fault orientation, which is especially important for understanding the earthquakes that occurred shortly after the impoundment and at more than 10 km distance from the reservoir. The combination of these two effects can induce positive Coulomb stress change over a larger area, which overlaps the majority of the events after the impoundment. While the causal relationship between the impoundment and seismicity warrants further analysis, we hope to inform the regional seismic impact of impoundment with this timely study.