Natural disasters such as earthquakes have consecutive impacts on the smart grid because of aftershock activities. To guarantee service requirements and smart grid stable operations, it is a challenge to design a fast and survivable rerouting mechanism. There are few studies that consider concurrent rerouting aiming at multiple services in smart grid communication network, however. Firstly, we formulate the node survivability, link survivability, and path survivability model in terms of the distance from the epicenter to the node and the link of the network. Meanwhile, we introduce the indicator of site difference level which is unique in the smart grid to further restrict the service path. Secondly, to improve the algorithm efficiency and reduce rerouting time, the deep first search algorithm is utilized to obtain the available rerouting set, and then the I-DQN based on the framework of reinforcement learning is proposed to achieve concurrent rerouting for multiple services. The experimental results show that our approach has a better convergence performance and higher survivability as well as the approximate latency in comparison with other approaches.