This paper proposes a maximum power point tracking (MPPT) and voltage regulation method based on model predictive control (MPC) for the two-stage grid-tied photovoltaic (PV) system, which can achieve MPPT and output voltage regulation of a PV system simultaneously. The MPPT algorithm based on MPC is implemented in a DC-DC boost converter. The reference voltage at maximum power point is obtained by dual step Incremental Conductance (I&C) algorithm under the rapidly varying illumination intensity, and the MPPT controller only needs to minimize one cost function of PV current, without pulse width modulation (PWM) module. To inject the generated PV power into the grid with high quality, this paper designs voltage regulation controller based on MPC to maintain the output voltage of the PV system at the desired value. The MPC controller outputs the optimal duty signal with the input and state constraints in the inner loop, and the PI controller in the outer loop is designed to improve the dynamic performance. The proposed method based on MPC was demonstrated using the SimPower systems tool in MATLAB/Simulink. Analysis and simulation results for the PV system show possible improvements on the closed-loop performance such as fast response and low overshoot.