In order to ensure the network operating life and avoid the disadvantages about the high energy consumption and high time delay in traditional node selection techniques, a new node stability selection technique of network topology control was proposed. The EETCA network topology structure was set up and researched the control of network topology by this technique. The network topology control process mainly included the cluster-head selection phase, the cluster establishment phase and the stable data transmission. The node selection model was established, and the retrieval range was reduced by Hopfield network model. Combined genetic algorithm with local search method of Hopfield network, the stability of network nodes was completed. Hopfield network local search method was used to generate the parent gene pool. The fitness of each chromosome was obtained. The genetic operator was determined, which generated the filial generation gene pool. The optimal solution and the node stability selection results were obtained. Experimental results show that the proposed technique can ensure the lifetime of the network. It has the low time delay and energy consumption.