Abstract: One of the interesting and difficult problems in recent reinforcement learning （RL） is to solve large scale state space problem. The basic principle on forgetting in memory psychology has been combined with value based reinforcement learning, thus generating a class of forgetting algorithms suitable to overcoming the RL problems. In this paper, the basic concepts for solving Markov decision problems are briefly introduced, the differences between off policy and on policy algorithms are compared, and the standard SARSA（λ） method is also outlined. After some characteristics of human memory and forgetting are analyzed, a forgetting rule for the RL agent is proposed, and then the SARSA（λ） algorithm is improved so as to form a Forget SARSA（λ） with forgetting function. Finally, the experimental results are presented.