Thermal drift-caused current measurement offset error usually results in unfavorable torque ripples of fundamental frequency, and hence a compensation method for current offset error is proposed in this article, which is initially derived based on the nonsalient-pole machines and then extended to the salient-pole machines. By filtering the difference between the predicted currents from a simple nominal model and the measured currents, the offset error is directly estimated and then compensated with minimal effects on the current dynamics. It is proved that the estimation is accurate if the filter has unity gain at the frequency of the offset error. Therefore, the proposed method is free of the current regulator type and shows strong robustness against machine parameter deviations. It can also stably work even when the output voltage is saturated. Two kinds of filters are designed in the stationary reference frame, and the low-pass filter with low bandwidth is recommended for its easy implementation. Finally, the effectiveness of the proposed method is verified by simulations and experiments.