Recently, model predictive control has been widely used to control grid-connected inverters due to its advantages. However, the conventional model predictive control methods usually require two AC voltage and current sensors to sample the grid voltages and currents. Particularly, the DC voltage sensor is also required to calculate the values of the voltage vectors. The inverter will lose its stability once these sensors fail. Thus, in this study, to improve the operational reliability of the gridconnected inverters, a sliding mode observer-based AC voltage sensorless model predictive control is proposed. First, a sliding mode observer is designed to estimate the grid voltage. Next, a new adaptive compensation strategy is proposed to remove the phase and amplitude errors caused by the low-pass filter. The main novelty of this compensation strategy is that it is immune to the actual grid frequency. Therefore, the grid voltage can be identified accurately, even under frequency deviation conditions. Besides, the stability and parameter designing method of the sliding mode observer is also analysed to provide a theoretical basis for its implementation. Finally, based on the observed grid voltage, the AC voltage sensorless model predictive control is achieved. Detailed comparative experimental results show the validity of the proposed method.