Until recently, in the literatures of discussing the fault tolerance problem of neural networks, the tolerance about input noise is mainly concerned. The problem is generally transformed into that of optimization and solved by some well-known optimization approach. But only a few dealt with the tolerance due to the network structural failure, i.e., the structural fault tolerance. In the paper, the structural fault tolerance is analyzed by using the covering algorithms. The necessary and sufficient conditions of allowing of single node failure in a neural network and the algorithm for constructing such a network are given. These results reveal the essence of the structural fault tolerance capacity and show a new way for the analysis of the fault tolerance of neural networks.