Abstract: A new Hopfield neural network approach for job-shop scheduling problems (JSP) is proposed. All constraints of job shop scheduling problems and its permutation matrix expression are proposed. A new computational energy function including all constraints of job-shop scheduling problem is given. A corresponding new Hopfield neural network construction and its weights of job-shop scheduling problem are given. To avoid the Hopfield neural network convergence to a local minimum to produce non feasible scheduling for JSP, the simulated annealing algorithm is applied to the Hopfield neural network and the network converges to a minimum volume O, making the steady outputs of the neural network as feasible solution for job shop scheduling problem. Compared with the existing methods, our modified method can keep the steady outputs of neural networks as feasible solution for job-shop scheduling problem.