Decentralized multi-agent control has broad applications, ranging from multi-robot cooperation to distributed sensor networks. In decentralized multi-agent control, systems are complex with unknown or highly uncertain dynamics, where traditional model-based control methods can hardly be applied. Compared with model-based control in control theory, deep reinforcement learning (DRL) is promising to learn the controller/policy from data without the knowing system dynamics. However, to directly apply DRL to decentralized multi-agent control is challenging, as interactions among agents make the learning environment non-stationary. More importantly, the existing multi-agent reinforcement learning (MARL) algorithms cannot ensure the closed-loop stability of a multi-agent system from a control-theoretic perspective, so the learned control polices are highly possible to generate abnormal or dangerous behaviors in real applications. Hence, without stability guarantee, the application of the existing MARL algorithms to real multi-agent systems is of great concern, e.g., UAVs, robots, and power systems, etc. In this paper, we aim to propose a new MARL algorithm for decentralized multi-agent control with a stability guarantee. The new MARL algorithm, termed as a multi-agent soft-actor critic (MASAC), is proposed under the well-known framework of “centralized-training-with-decentralized-execution”. The closed-loop stability is guaranteed by the introduction of a stability constraint during the policy improvement in our MASAC algorithm. The stability constraint is designed based on Lyapunov’s method in control theory. To demonstrate the effectiveness, we present a multi-agent navigation example to show the efficiency of the proposed MASAC algorithm.