This study designed a system consisting of a photovoltaic system and a DC-DC boost converter with buck-boost inverter. A multi-error method, based on model predictive control (MPC), is presented for control of the buck-boost inverter. Incremental conductivity and predictive control methods have also been used to track the maximum power of the photovoltaic system. Due to the fact that inverters are in the category of systems with fast dynamics, in this method, by first determining the system state space and its discrete time model, a switching algorithm is proposed to reduce the larger error for the converter. By using this control method, in addition to reducing the total harmonic distortion (THD), the inverter voltage reaches the set reference value at a high speed. To evaluate the performance of the proposed method, the dynamic performance of the converter at the reference voltage given to the system was investigated. The results of system performance in SIMULINK environment were simulated and analyzed by MATLAB software. According to the simulation results, we can point out the advantage of this system in following the reference signal with high speed and accuracy.