The complementary operation of hydro-photovoltaic (PV) hybrid power plants has become important in the modern power systems. However, the strong variations involved in the streamflow and PV generation lead to uncertainties in the complementary operations. To improve the long-term complementary operation performance of a large-scale hydro-PV hybrid power plant, this study developed long-term stochastic optimization methods that simultaneously consider the uncertainty of the streamflow and PV power output. A multi-objective optimization model was established to maximize the total energy production and guaranteed rate. The model was then solved using stochastic dynamic programming to obtain the operation decisions (carryover storage), which are functions of the initial storage, streamflow, and PV output. Finally, four schemes for deriving the operation rules were constructed: (1) stochastic optimization of the hydropower station directly plus PV output, (2) stochastic optimization of the hydro-PV hybrid power plant considering stochastic streamflow and deterministic PV output, (3) stochastic optimization of the hydro-PV hybrid power plant considering independent stochastic streamflow and PV output, and (4) stochastic optimization of the hydro-PV hybrid power plant considering correlative stochastic streamflow and PV output. The proposed methods were applied to the Longyangxia hydro-PV hybrid power plant in Qinghai province, China, which is the largest hydro-PV plant in the world. The performance of the four schemes was compared across calibration and validation periods. The results show that: (1) the complementarity of hydropower and PV power in long-term operations is highly necessary, (2) considering the uncertainty of stochastic streamfiow and PV output simultaneously improves the efficiency of complementary operations, and (3) stochastic optimization of the hydro-PV hybrid power plant considering the independent stochastic streamflow and PV output gives the best performance in this particular case study. Specifically, compared to conventional operations, the total generation and total guaranteed rate could be increased by 3.18% and 10.63%, respectively, in the calibration period, and by 6.66% and 22.92%, respectively, in the validation period. Thus, the proposed stochastic optimization method is helpful in improving the long-term complementary operation of large-scale hydro-PV hybrid power plants.