Reinforcement learning is a kind of unsupervised learning methods that an agent control rules from experiences acquired by interactions with environment. The eligibility is used to resolve the credit-assignment problem which is one of important problems in reinforcement learning, Conventional eligibilities such as the accumulating eligibility and the replacing eligibility are ineffective in use of rewards acquired in learning process, since on1y one executed action for a visited state is learned. In this paper, we propose a new eligibility, called the distributed eligibility, with which not only an executed action but also neighboring actions in a visited state are to be learned. The fuzzy Q-learning algorithm using the proposed eligibility is applied to a cart-pole balancing problem, which shows the superiority of the proposed method to conventional methods in terms of learning speed.