In order to solve the problems of power and frequency fluctuations and harmonic content in the output voltage occurring in the grid-connected PV under the traditional virtual synchronous generator control, a VSG rotational inertia adaptive control method and a modulation scheme with stochastic excitation are introduced in the grid-connected. A voltage control loop with virtual impedance is introduced in the VSG control and combined with a current control loop based on a quasi-proportional resonant controller to construct a VSG control strategy for grid-connected inverters of PV power systems. With this strategy, the THD of the three-phase voltages A, B and C decreased by 15.17%, 15.37% and 13.10%, respectively, and the active power overshoot decreased by 7.42% in simulation results, and the THD of the three-phase voltages A, B and C decreased by 1.92%, 4.61% and 2.44%, respectively, in experimental results, and the frequency was stabilized at 50.07 Hz. The simulation and experimental results demonstrated that the proposed method can effectively suppress the power and frequency oscillations and reduce the THD of output voltage, which verifies the feasibility of the proposed method.