Photovoltaic (PV) power generation can help reduce households’ electricity from the power grid and thus reduce electricity bills. However, due to the intermittence and time-varying nature of PV power generation, part of the clean energy will be wasted. Especially in some places where PV power is allowed to be sold to the power grid, the PV power that exceeds the feed-in limit will be curtailed to reduce the pressure on the infrastructure of the power grid. Battery energy storage systems (BESSs) as energy buffers have attracted increasing attention to help improve the penetration of PV power to households. This paper presents an adaptive energy management method to minimize the energy cost of residential PV-battery systems. First, the uncertainty of the predictive electricity demand and PV power supply is modeled. Then a stochastic model predictive control (SMPC) strategy is used to determine the optimal power flow of the system. Due to the deviation between the predictive input values and the actual ones, the power flow from SMPC is adjusted based on the improved correction strategy (ICS) proposed in this paper. By comparing with the other two methods (one considers the uncertainty and the other does not), the proposed method can increase the economic benefits of the system by 18% and 63%, respectively. The wasted PV power that exceeds the feed-in limit can also be reduced by 24% and 31%. This verifies the effectiveness of the proposed method to improve the system's economic benefits and self-consumption of clean energy.