With the rapid development of large language models (LLMs), it is highly demanded that LLMs can be adopted to make decisions to enable the artificial general intelligence. Most approaches leverage manually crafted examples to prompt the LLMs to imitate the decision process of human. However, designing optimal prompts is difficult and the patterned prompts can hardly be generalized to more complex environments. In this paper, we propose a novel model named Large Decision Model with Memory (LDM²), which leverages a dynamic memory mechanism to construct dynamic prompts, guiding the LLMs in making proper decisions according to the faced state. LDM² consists of two stages: memory formation and memory refinement. In the former stage, human behaviors are decomposed into state-action tuples utilizing the powerful summarizing ability of LLMs. Then, these tuples are stored in the memory, whose indices are generated by the LLMs, to facilitate the retrieval of the most relevant subset of memorized tuples based on the current state. In the latter stage, our LDM² employs tree exploration to discover more suitable decision processes and enrich the memory by adding valuable state-action tuples. The dynamic circle of exploration and memory enhancement provides LDM² a better understanding of the global environment. Extensive experiments conducted in two interactive environments have shown that our LDM² outperforms the baselines in terms of both score and success rate, which demonstrates its effectiveness.