For sensorless control of permanent magnet synchronous motors (PMSM), the model-based method is often used in medium- and high-speed range due to its simplicity and flexibility. However, the 6th harmonic of the estimated back electromotive force (BEMF) caused by the dead-time effect and flux harmonic in estimated dq-axes lead to the ripple of the estimated speed and position. To address this problem, an observer based on a pre-designed transfer function is proposed with the backstepping-design method in this paper. The pre-designed transfer function can effectively suppress the 6th harmonic in estimated BEMF with second-order low-pass characteristics. Compared to the conventional dq-axes reduced-order observer, the proposed observer improves the suppression effect on the estimated BEMF 6th harmonic by increasing the order of the equivalent filter. The effectiveness of the proposed observer is verified through a 2.2 kW PMSM platform.