DC offsets, odd harmonics and even harmonics are unavoidable in PMSM drives, which affect the performance of sensorless control for PMSM drives. To resolve this problem, a novel sensorless control is proposed in this paper. It makes use of the basic trigonometric function and arithmetic operation between multiple consecutive sampled signals to estimate the speed and has the ability to suppress DC offsets, odd harmonic and even harmonic. The proposed method is composed of nonlinear flux observer (NFO), zero crossing detection (ZCD) module and adaptive multiple-consecutive-samples frequency estimation (AMCS-FE) module. NFO is used to observe rotor flux, ZCD module realizes system adaptivity, and AMCS-FE module serves for speed estimation. The simulation results in MATLAB/Simulink demonstrate the feasibility of the proposed method.