To improve pure integral calculations with integral drift and dc bias, and poor dynamic response under conventional direct power control, a grid-voltage sensorless predictive current control strategy of three-phase PWM rectifier is proposed. In the voltage sensorless control algorithm, an improved virtual flux observer is constructed by introducing bandstop filter feedback to solve the dc bias. Moreover, to address the inaccurate voltage-vector selection algorithm in the two-step prediction, Lagrange interpolation is introduced to make the predictive current more accurate. Experimental results verify that the three-phase PWM rectifier with the proposed strategy can achieve high power factor, high prediction accuracy and improve dynamic performance of the system.