A recommender system aims to recommend items that a user is interested in among many items. The need for the recommender system has been expanded by the information explosion. Various approaches have been suggested for providing meaningful recommendations to users. One of the proposed approaches is to consider a recommender system as a Markov decision process (MDP) problem and try to solve it using reinforcement learning (RL). However, existing RL-based methods have an obvious drawback. To solve an MDP in a recommender system, they encountered a problem with the large number of discrete actions that bring RL to a larger class of problems. In this paper, we propose a novel RL-based recommender system. We formulate a recommender system as a gridworld game by using a biclustering technique that can reduce the state and action space significantly. Using biclustering not only reduces space but also improves the recommendation quality effectively handling the cold-start problem. In addition, our approach can provide users with some explanation why the system recommends certain items. Lastly, we examine the proposed algorithm on a real-world dataset and achieve a better performance than the widely used recommendation algorithm.