Network slicing enables multiple virtual networks run on the same physical infrastructure to support various use cases in 5G and beyond. These use cases, however, have very diverse network resource demands, e.g., communication and computation, and various performance metrics such as latency and throughput. To effectively allocate network resources to slices, we propose DeepSlicing that integrates the alternating direction method of multipliers (ADMM) and deep reinforcement learning (DRL). DeepSlicing decomposes the network slicing problem into a master problem and several slave problems. The master problem is solved based on convex optimization and the slave problem is handled by DRL method which learns the optimal resource allocation policy. The performance of the proposed algorithm is validated through network simulations.