Model predictive control has been widely used in the industry. This can control the multivariable system with constraints on input and output variables but it needs online computation solver, and creates the nonconvex solution in nonlinear plant due to the parameter uncertainties. The online computational problem and non-convex solution of the model predictive control are achieved via neural network model predictive control. The paper explores the speed control of permanent magnet synchronous motor (PMSM) by using neural network model predictive control (NNMPC) technique. The multi-layer artificial neural network is used to identify the dynamics of PMSM. The set point speed tracking control of PMSM is identified by using neural network model predictive control strategy. By using the set of input and output data obtained from the system, the multi input-output feed-forward neural network model is created. Levenberg-Marquardt algorithm is used to train the process models of the PMSM. That provides future plant output for control optimization of the predictive control. The overall system is developed and tested in the MATLAB/Simulink. To evaluate the efficiency of the controller proposed, it is compared with a constrained model predictive controller through the studies of simulation. The overshoot and settling time of the speed response of the PMSM are measured and analyzed for NNMPC and constrained MPC.