Abstract: In traditional artificial neural network model, the activation functions of neurons in the same hidden layer are the same, which is not consistent with the actual situation of human neurons. For this reason, and a forward neural network model with different activation functions of each neuron in the hidden layer was constructed, a cluster of Chebyshev orthogonal polynomials was used as the activation function of each neuron of the hidden layer (Chebyshev forward neural network). A training algorithm for network parameters based on gradient descent method was derived for Chebyshev feedforward neural network. The simulation experiment shows that the Chebyshev forward neural network algorithm based on gradient descent method can effectively adjust the network parameters, and make it approximate in sample data set of complex patterns with high precision.