Abstract: To restrain the torque fluctuations of permanent magnet synchronous motor(PMSM), a PMSM torque ripple suppression method is proposed based on the construction of fractional-order global sliding mode controller and flux observer of Elman neural network resistance identification. Firstly, the mathematical model of PMSM is established, the fractional sliding mode surface was established based on the flux and torque error, and a fractional global sliding mode controller is designed. Secondly, in order to further suppress the torque ripple by observing the flux linkage accurately, a resistance identification method of Elman neural network is proposed. Then, the identification results were used to design the flux observer, and combined with the fractional-order global sliding mode controller, a PMSM control system based on fractional-order global sliding mode and flux observation is constructed. It can suppress the torque ripple of PMSM. Experimental results show that the proposed method, which is based on the construction of fractional global sliding mode controller and the flux observer based on Elman neural network resistance identification, can suppress the torque ripple well.