In this paper, a grid voltage sensorless model predictive control is proposed and verified by simulation and experimental tests for a PWM rectifier. The presented method is simple and cost effective due to no need of modulator and voltage sensors. The developed sliding mode voltage observer (SMVO) can theoretically track the grid voltage accurately without phase lag and magnitude error. Based on the proposed SMVO, the finite control set-model predictive control (FCS-MPC) is incorporated for power regulation. The active power and reactive power are calculated and predicted using the measured current and the estimated grid voltage from the SMVO. With the predicated power for one-step delay compensation, the best voltage vector minimizing the tracking error is selected by FCS-MPC. The whole algorithm is implemented in stationary frame without using Park's transformation. Both the simulation and experimental results validate the effectiveness of the proposed method.