The back electromotive force (BEMF) observer is an effective model-based method for the permanent magnet synchronous motor (PMSM) sensorless drive in medium- and high-speed range. However, the conventional BEMF observers have inherent defect in dc-bias elimination, resulting in the fundamental frequency fluctuation of the estimated position. To address the problems, a minimum-order BEMF observer is proposed using the backstepping design method. First, an expected transfer function is designed to realize the band-stop elimination on dc-bias. Then, the backstepping design method is used to obtain the observer state equation, which is the minimum-order time-domain implementation of the equivalent transfer function. Compared with the conventional reduced-order observer, the elimination capability on dc-bias is enhanced of the studied observer. Due to directly estimating the BEMF without estimating the current, the computation resource of the system can be saved. The effectiveness of the studied sensorless algorithm is verified on a 2.2-kW PMSM platform.