The stability of PWM rectifiers with a deadbeat current controller is seriously influenced by computation time delays and low-pass filters inserted into the current-sampling circuit. Predictive current control is often adopted to solve this problem. However, grid current predictive precision is affected by many factors such as grid voltage estimated errors, plant model mismatches, dead time and so on. In addition, the predictive current error aggravates the grid current distortion. To improve the grid current predictive precision, an improved deadbeat current controller with a repetitive-control-based observer to predict the grid current is proposed in this paper. The design principle of the proposed observer is given and its stability is discussed. The predictive performance of the observer is also analyzed in the frequency domain. It is shown that the grid predictive error can be decreased with the proposed method in the related bode diagrams. Experimental results show that the proposed method can minimize the current predictive error, improve the current loop robustness and reduce the grid current THD of PWM rectifiers.