In order to learn in dynamic environments, reinforcement learning algorithms like Q-learning, TD(0)-learning, TD(λ)-learning have been proposed. however, most of them have a drawback of very slow learning because the reinforcement value is given when they reach their goal state. In this thesis, we have proposed a reinforcement learning method that can approximate fast to the goal state in maze environments. The proposed reinforcement learning method is separated into global learning and local learning, and then it executes learning. Global learning is a learning that uses the replacing eligibility trace method to search the goal state. In local learning, it propagates the goal state value that has been searched through global learning to neighboring sates, and then searches goal state in neighboring states. we can show through experiments that the reinforcement learning method proposed in this thesis can find out an optimal solution faster than other reinforcement learning methods like Q-learning, TD(o)learning and TD(λ)-learning.