Smart grid is one of the representative applications for 5G network. In this scenario, different business types of smart grid have diverse requirements in service quality, isolation level, and maintenance management. Moreover, the quantity, location and distribution of 5G terminals lack a comprehensive prior description. To improve resource utilization efficiency and reduce the operating cost of power companies, real-time resource management for network slicing has become an urgent problem to be solved. In this paper, we propose a slice request allocation method for smart grid based on the framework of deep reinforcement learning. We innovatively encode the allocated and free resources with the slice request into a unified tensor, and then design the corresponding action and reward function. We employ the deep reinforcement learning ACKTR algorithm based on the actor-critic framework to find the optimal decision policy. The simulation experiments show that compared with the previous slice resource allocation methods based on Q-learning and Deep Dueling, our method can achieve better long-term rewards and effectively improve the utilization efficiency of 5G network for smart grid.