Abstract: According to Fourier series approximation theory,a single-input multiple-output(SIMO) trigonometrically-activated Fourier neural network model is constructed by setting the hidden-layer neuron activation function as orthogonal trigonometric function series and selecting the periodical parameter of these activation functions properly.In light of the characteristics of the presented network,a pseudo-inverse based weights-direct-determination method is derived to determine the optimal weights of the network with one step,and a structure-automatic-determination algorithm is designed.Simulation results substantiate that,compared with the traditional BP(backpropogation) neural network and the SIMO Fourier neural network model based on least square method,this model has higher accuracy and faster computing speed.