This article addresses the grid-connected single-phase photovoltaic (PV) inverter control. A long-horizon finite-set model predictive control (MPC) strategy is proposed to control the voltage source inverter. To achieve this, a multi-step implementation approach and a control sequence rearrangement method are designed to reduce the sampling frequency and switching frequency. The optimization problem for the finite-set MPC is further simplified to reduce the computational complexity of the optimization procedure. Moreover, a multi-step delay compensation method is developed to compensate for the computational delay of the control algorithm. Finally, the proposed control method is implemented in a grid-connected PV inverter and simulation test results demonstrate its effectiveness under different load and generation conditions.