For single-phase photovoltaic grid system, taking the circuit topology of double-stage single-phase grid inverter as a core, this paper establishes the mathematical model, and builds the simulation model of 5 kW single-phase grid inverter system in Matlab/Simulink environment. MPPT algorithm based on the observation of the disturbance voltage and double loop control strategy based on feedforward are adopted, whose properties are studied and simulated. With Matlab language, MPPT algorithm is programmed as a function which can simulate the illumination change, and the simulation analysis of illumination invariant and illumination change is respectively carried out. The simulation results show that it not only makes system have better stability and fast dynamic response characteristics, but also realizes the target that the output voltage has the same frequency and phase with inverted current and lower total harmonic distortion rate (THD less than 1%).