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Selecting the output voltage of the photovoltaic micro-grid inverter as the control signal and the output current as the output one, and considering the equivalent resistance of the circuit, the circuit of the single-phase photovoltaic micro-grid inverter is simplified and its working principle is analyzed. Then, its differential equation is created based on the voltage loop equation. Then the fourth-order Runge-Kutta iterative model for the solve equation is created. After simplifying and discretizing the analytic solutions of the differential equation, the expression of the output control signal of the inverter is obtained through the linear predictive control method and finally the numerical simulation and analysis are conducted. Through numerical simulation, the output voltage and current waveforms in both time and frequency domain which belong to the inverter are analyzed, and the error signals of output current are measured. The results show that: The model of single-phase photovoltaic micro-grid inverters and the iterative model for the solve equation are effective. Under the condition of 1 mH coupling inductance and 10 KHz switching frequency, the voltage of and the total harmonic distortion of the output current of the inverters are 1.76% and 3.99% respectively. The peak ripple of its output voltage is 50V, but the total harmonic distortion of its output signal meets the requirements of the standard of national grid connection (≤5%).