Computer network is one of the most important equipment in the whole world, with the gradual and rapid development of its scale, how to manage and maintain the computer network is becoming more and more complicated. The network fault diagnosis has become people’s focus. With the development of artificial intelligence, by introducing neural network technology into the area of network fault diagnosis, neural network can bring out its advantages in the fault diagnosis. This article would employ SOM neural network and BP neural network, the samples would be clustered by using SOM neural network, and the results of the cluster would be put back into the original samples, which would also be set with certain weights, through the weights’ consistent updating, the convergence speed of BP neural network can be improved. Through using LM algorithm to improve BP neural network and using computer network diagnosis as practical samples to simulate and analyze computer, the validity of this method has been proved, and at the same time building a system of computer network diagnosis can be very meaningful for theoretical study and practical use.