Abstract: Based on Fourier series principle, the single input, multiple outputs (SIMO) Fourier neural networks are proposed. The SIMO Fourier neural networks turn nonlinear mapping relationship into linear mapping relationship, turn the method of solving neural networks' weights from the nonlinear optimization method to linear optimization method, and use the least square method to compute the weights of the network. So, the SIMO Fourier neural networks highly improve the convergence speed and avoid local minima problem. When the training output samples are affected by white noise, the least square method have good denoising function.