A scheme of finite control set model predictive control (FCS-MPC) is proposed for the grid-connected stability of photovoltaic and storage microgrid. The bi-directional DC/DC converter of the energy storage system adopts voltage and current dual-loop control to stabilize the DC bus voltage. Then, the discrete mathematical model of the grid-connected inverter is established, and the output current of inverter is used as the cost function control variable to construct current predictive controller. Based on the prediction of the next two steps of inverter current, the vector angle compensation method is introduced to compensate for the delay of the control process. Finally, the simulation model of photovoltaic and storage microgrid is established by using MATLAB/Simulink, and the voltage and current responses under traditional method and MPC are compared and analyzed. Simulation results show that the proposed scheme can improve the DC bus voltage stability and reduce the grid-connected current distortion rate under load changes and photovoltaic power fluctuations.