The Permanent Magnet Synchronous Motor (PMSM) is widely used in many fields. Aiming at nonlinearity, strong coupling and uncertainty of the PMSM, this paper proposes a nonlinear multi-input multi-output (MIMO) decoupling PMSM algorithm based on Active Disturbance Rejection Control (ADRC). A Lower-Upper matrix factorization approach is introduced to solve a general inverse of the measured time-varying matrix in real-time decoupling ADRC. This PMSM is based on the vector control. First, the PMSM model and vector control are simulated. Then, a first-order ADRC is introduced and used to replace the PID controller in the d and q axis of PMSM respectively. The simulation shows that the replaced system has a smaller fluctuation, faster response and better stability. Finally, the nonlinear MIMO decoupling ADRC and its inverse matrix method are deduced. Then, the decoupling PMSM control based on ADRC is verified. The simulation shows that this system has a better static and dynamic performance, and it conforms to the PMSM characteristics better. All this shows that the nonlinear MIMO decoupling ADRC is a better strategy for the PMSM. The presented algorithm also has advantage in method compared with some recent results of decoupling PMSM control.