A deep learning algorithm using deep long short-term memory and genetic attention mechanism (DLSTM-GA) is proposed for the prediction of chaotic behavior of power system. With shared parameters, attention mechanism is added to optimize DLSTM model based on genetic algorithm. One can find potential characteristics in time sequence and avoid the local optimization. Inspired by evolutionary computation of optimization method, the method is a good way to learn parameters in the attention layer. It shows that the trained DLSTM-GA network not only has higher prediction accuracy than the reference model, but also has long-term prediction ability.