Aiming at the problem that the traditional PI control cannot guarantee the stability and accuracy of the system, a new quasi-Z-source inverter control method is proposed. For the DC side, the sliding mode control (SMC) method was proposed. It is based on the differences in capacitor voltage, inductor current and their integration. The derivation process of the DC chain voltage sliding mode control rate was analyzed. For the inverter side, an improved repetitive control method is adopted. The state space model of the standard repetitive controller was established. By using Lyapunov theory, the design limit of the state feedback control rule based on linear matrix inequalities was obtained. This allows for rapid response and precise tracking. In addition, the main circuit parameters for the grid connection of quasi-Z-source inverters in wind power systems have been designed. The simulation analysis proves the effectiveness of this control method. Compared with the traditional PI control, this method greatly improves the stability and control accuracy of the system.