Abstract: In this paper, Lyapunov energy function is constructed according to the Hopfield type neural network with infinite time delay. The stability of the network is proved using the Lyap-unov energy function. In the course of proving, the conclusion of lemma and the particularity of the function that is gotten is fully utilized. Some inequality analysis methods and inequality enlarg-ing and narrowing techniques are used. The Lyapunov functional is also invoved because of the existence of time delay.In the end, the conclusion of global consistent asymptotic stability for the network is drawn from the lemma.