This paper attempts to solve the optimal power allocation（OPA） problem for smart grid system in a new distinguished way.Conventionally the numerical optimization approaches including traditional convex optimization and heuristic search methods almost occupy the addressing of such problem.However,these optimization algorithms may suffer from high computational complexity when the system scales up,which would inevitably create a gap between the theoretical algorithm design and real-time algorithm implementation.In this paper,we aim to provide a new learning based approach to handle the real-time OPA problem in smart grid system.The key idea behind this approach is to treat the input and output of traditional OPA optimization algorithm as an unknown nonlinear mapping,which is then approximated by recent popular learning based tools such as deep neural network（DNN）.As long as the constructed DNN can accurately learn such nonlinear mapping,then the OPA problem can be solved in real time.Our main contribution is to theoretically show that the traditional decentralized gradient-based optimization algorithm for OPA problem can be accurately approximated by a well-constructed DNN.Furthermore,experimental case studies validate the effectiveness and advantages of our proposed method.