Scheduling jobs on identical machines is a situation frequently encountered in various manufacturing systems. In this paper, a new coupled transiently chaotic neural network (CTCNN) is put forward to solve identical parallel machine scheduling. A mixed integer programming model of this problem is transformed into a CTCNN computation architecture by introducing a permutation matrix expression. A new computational energy function is proposed to express the objective besides all the constraints. In particular, the tradeoff problem existing among the penalty terms in the energy function is overcome by using time-varying penalty parameters. Finally, results tested on 3 different scale problems with 100 random initial conditions show that the network converges and can solve these problems in the reasonable time.