The multi-stage group decision making problem is a typical sequential group decision making problem. It is normally utilized to find the optimal solution to the group decision problems in discrete deterministic environment. However, the real life environments faced by decision-makers are usually full of uncertainty, even unknown environments (with unknown state transition matrix). Therefore, it is essential for the decision-makers to obtain more information by interacting with the environment dynamically to achieve an optimal decision strategy with high consensus degree. Due to the advantage of reinforcement learning in handling the sequential decision-making problems, the classical reinforcement learning algorithm (Q-learning) is improved to discover the optimal solution of multi-stage group decision making problems under uncertain environment. Additionally, a theorem is proposed to show that the optimal group decision obtained by using the improved Q-learning algorithm is the group decision with the highest degree of group consensus. Finally, an illustrative example is presented to verify the rationality and feasibility of the proposed algorithm.