Federated Learning (FL), hailed as a potent approach in merging medical expertise, promises to elevate collaborative efforts among healthcare institutions while safeguarding the privacy and security of sensitive medical data, thereby energizing the trajectory of intelligent healthcare advancements. However, the diversity in training objectives across medical institutions can diminish their active participation in a unified federated training process. To address this issue of waning enthusiasm due to diverse training goals, in this paper, we propose Personalized Medical Federated Learning method based on Mutual Distillation Knowledge (pFedMKD). Specifically, we propose a similarity-based mutual distillation model selection algorithm that reduces interference among medical institutions with notably diverse data distributions. Moreover, we develop a server-side local model update method leveraging mutual knowledge distillation, enabling each local model to gain beneficial insights for personalization from analogous models. Additionally, we formulate a personalized model update method utilizing knowledge distillation from specifically labeled samples, thereby improving the performance of personalized models. Experimental results demonstrate that compared to the baseline algorithm, pFedMKD can more effectively address the target heterogeneity problem among different medical institutions, enabling each institution to achieve higher personalized performance in federated learning tasks.