With the rapidly increasing number and movement of satellites, the ground stations scheduling problem for Low Earth Orbit (LEO) satellites becomes more complex due to its over-constraint nature. In this paper, we propose a novel ground stations scheduling algorithm named Reinforcement Learning-Based Ground Stations Scheduling Algorithm (RLBGSSA). Its batch tasks planning branch (RLBGSBSA) ensures ground stations efficiently track satellites and achieve timeliness. Under the state constraints, the individual task planning branch of RLBGSSA (RLBGSISA) generates the feasible planning combinations based on reinforcement learning, and gains the combination constraints to filter the planning combinations. To maintain the stability of tasks and equipment, the optimal combination among the screened results is selected via a designed value function, which can achieve minimal changes to planned tasks. Furthermore, RLBGSBSA can reset the scheduling of ground stations to void planning overflow, when the number of individual tasks newly added is too large. Finally, the rationality and effectiveness of our algorithm are verified by numerical simulation.