This paper presents a novel, simple and robust AC voltage sensorless predictive control method for the active front end (AFE) rectifiers. The proposed sensorless control is based on computing the input AC voltage from the instantaneous active and reactive powers using the input AC currents, DC link voltage, and the switching state. The proposed sensorless predictive control has suitable results even with the imprecise value of the input inductance. However, the precise estimation of the input inductance improves the robustness of the method. Therefore, a novel inductance estimation method is proposed based on model reference adaptive system (MRAS) observers for parameter estimation. The proposed MRAS observer is based on input AC current. The feasibility and the robustness of the method has been confirmed through the computer simulations.