When the weight functions of the continuous process neural network are expanded by orthogonal basis, the number of the basis function can not be determined effectively. The continuous process neural network has lower approach accuracy. Therefore, a discrete process neural network is presented. The three spline numerical integration is applied to deal with the aggregation of discrete samples and weights in time-domain. The double chain quantum particle swarm algorithm is used to the global optimization of model parameters. The evolution of the population is executed by the quantum rotation gate and quantum not gate. The extreme learning algorithm is applied to the local search and the output weights are computed by the Moore-Penrose inverse. The results of the simulation experiment based on the time sequence prediction verify the effectiveness of the proposed model, and show that the capability of training convergence and accurate approximation are improved at a certain degree.