Aiming at the problems of low computational efficiency and insufficient accuracy in the privacy-preserving neural network based on homomorphic encryption， an efficient Homomorphic Neural Network （HNN） under three-party collaborative supporting privacy-preserving training was proposed. Firstly， in order to reduce the computational cost of ciphertext-ciphertext multiplication in homomorphic encryption， the idea of secret sharing was combined to design a secure fast multiplication protocol to convert the ciphertext-ciphertext multiplication into plaintext-ciphertext multiplication with low complexity. Then， in order to avoid multiple iterations of ciphertext polynomials generated during the construction of HNN and improve the nonlinear calculation accuracy， a secure nonlinear calculation method was studied， which executed the corresponding nonlinear operator for the confused plaintext message with random mask. Finally， the security， correctness and efficiency of the proposed protocols were analyzed theoretically， and the effectiveness and superiority of HNN were verified by experiments. Experimental results show that compared with the dual server scheme PPML （Privacy Protection Machine Learning）， HNN has the training efficiency improved by 18.9 times and the model accuracy improved by 1.4 percentage points.