Network slicing enables the multiplexing of independent logical networks on the same physical network infrastructure to provide different network services for different applications. The resource allocation problem involved in network slicing is typically a decision-making problem, falling within the scope of reinforcement learning. The advantage of adapting to dynamic wireless environments makes reinforcement learning a good candidate for problem solving. In this paper, to tackle the constrained mixed integer nonlinear programming problem in network slicing, we propose an augmented Lagrangian-based soft actor–critic (AL-SAC) algorithm. In this algorithm, a hierarchical action selection network is designed to handle the hybrid action space. More importantly, inspired by the augmented Lagrangian method, both neural networks for Lagrange multipliers and a penalty item are introduced to deal with the constraints. Experiment results show that the proposed AL-SAC algorithm can strictly satisfy the constraints, and achieve better performance than other benchmark algorithms.