This study addresses the problem of autonomous rear parking (ARP) for car-like nonholonomic vehicles. ARP includes path planning to generate an efficient collision-free path from the start point to the target parking slot and path following to produce control inputs to stably follow the generated path. This paper proposes an efficient ARP method that consists of the following five components: (1) OpenAI Gym environment for training the reinforcement learning agent, (2) path planning based on rapidly exploring random trees, (3) path following based on model predictive control, (4) reinforcement learning based on the Markov decision process, and (5) travel length estimation between the start and the goal points. The evaluation results in OpenAI Gym show that the proposed ARP method can successfully be used by minimizing the difference between the reference points and trajectories produced by the proposed method.