This paper presents the design model and simulation of a double-stage single-phase grid-connected PV system. This system includes an MPPT DC-DC boost power converter and a transformer-less single-phase DC-AC power inverter, which is connected to the power grid with an LCL filter. In the DC-DC boost converter, the Perturb and Observe algorithms are combined. The output voltage of the DC-DC converter is regulated, and the DC/AC output voltage is synchronized with the grid. The MATLAB-Simulink environment is used for the closed-loop simulation of the proposed setup. The simulation results are presented for various solar irradiance conditions and show that photovoltaic current is generated and matches the phase of grid voltage.