Abstract: To enhance approximation ability and computation efficiency of multi-aggregation process neural networks (MAPNN), a training algorithm based on numerical integration is proposed. First, the input functions and the weight functions are discretized, and then the multi-integrations of product of input functions and weight functions are obtained by employing the combined trapezoidal integration or the combined Simpson integration. The MAPNN's parameters are adjusted by the Levenberg-Marquardt algorithm. The simulation results show that the approximation ability and the computation efficiency of the proposed algorithm are obviously superior to that of the orthogonal basis expansion method, which reveals that the proposed approach is an effective way to improve the approximation ablity and the computation efficiency of MAPNN.