Associative memory engages in the integration of relevant information for comprehension in the human cognition system. In this work, we seek to improve alignment between language models and human brain while processing speech information by integrating associative memory. After verifying the alignment between language model and brain by mapping language model activations to brain activity, the original text stimuli expanded with simulated associative memory are regarded as input to computational language models. We find the alignment between language model and brain is improved in brain regions closely related to associative memory processing. We also demonstrate large language models after specific supervised fine-tuning better align with brain response, by building the Association dataset containing 1000 samples of stories, with instructions encouraging associative memory as input and associated content as output.