Aiming at the defects of filtering precision limitation and low efficiency in using the existing nonlinear filtering algorithms for neural network training, a novel neural network training algorithm based on the cubature Kalman filter is proposed. Firstly, the state space model of the neural network is established. Then the network connection weights are used as the state of the system’s parameters, and the training process of neural network weights is realized by a set of cubature points produced by adopting the third-order spherical-radial standards. The theoretical analysis and simulation results show the feasibility and effectiveness of the proposed algorithm.