In this paper, a new control method for quasi-Z-source cascaded multilevel inverter based grid-connected photovoltaic (PV) system using evolutionary algorithm and artificial neural network (ANN) is proposed. The proposed method is capable of boosting the PV array voltage to a higher level and solves the imbalance problem of DC-link voltage in traditional cascaded H-bridge inverters using ANN. The proposed control system adjusts the grid injected current in phase with the grid voltage and achieves independent maximum power point tracking (MPPT) for the separate PV arrays by proportional-integral (PI) controllers. For achieving the best performance, this paper presents an optimum approach to design the controller parameters using particle swarm optimization (PSO). The primary design goal is obtaining good response by minimizing the integral absolute error. Also, the transient response is guaranteed by minimizing the overshoot, settling time and rise time of the system response. The effectiveness of the new proposed control method has been verified through simulation studies in a seven level quasi-Z-source cascaded multilevel inverter.