Hysteresis model predictive control (HMPC) is a variant of finite-control-set model predictive control, which is mainly developed for high-power applications. In this paper, the HMPC scheme is proposed to control a high-power grid-connected two-level voltage source inverter with an inductive-capacitive-inductive (LCL) filter. To ensure the stable operation of the control system, the resonance characteristics of the system with an LCL filter based on HMPC are analyzed, and an active damping scheme is then given. On the other hand, the impacts of the modeling error on system stability and average switching frequency are analyzed in detail. Then, a new switching frequency-adaptive control scheme that uses the average switching frequency to adjust the parameter value of the predictive model online is presented. The new control scheme can keep the average switching frequency within an acceptable operational margin, while improving the stability of the control system. For demonstration, the proposed control scheme has been implemented on a small-scale grid-connected inverter system, and the results show that the theoretical analysis is correct and that the proposed control scheme is effective.