Title: Model-free Learning Control of Nonlinear Stochastic Systems with Stability Guarantee. Abstract: Reinforcement learning (RL) offers a principled way to achieve the optimal cumulative performance index in discrete-time nonlinear stochastic systems, which are modeled as Markov decision processes. Its integration with deep learning techniques has promoted the field of deep RL with an impressive performance in complicated continuous control tasks. However, from a control-theoretic perspective, the first and most important property of a system to be guaranteed is stability. Unfortunately, stability is rarely assured in RL and remains an open question. In this paper, we propose a stability guaranteed RL framework which simultaneously learns a Lyapunov function along with the controller or policy, both of which are parameterized by deep neural networks, by borrowing the concept of Lyapunov function from control theory. Our framework can not only offer comparable or superior control performance over state-of-the-art RL algorithms, but also construct a Lyapunov function to validate the closed-loop stability. In the simulated experiments, our approach is evaluated on several well-known examples including classic CartPole balancing, 3-dimensional robot control and control of synthetic biology gene regulatory networks. Compared with RL algorithms without stability guarantee, our approach can enable the system to recover to the operating point when interfered by uncertainties such as unseen disturbances and system parametric variations to a certain extent. 