Model editing aims to precisely modify the behaviours of large language models (LLMs) on specific knowledge while keeping irrelevant knowledge unchanged. It has been proven effective in resolving hallucination and out-of-date issues in LLMs. As a result, it can boost the application of LLMs in many critical domains (e.g., medical domain), where the hallucination is not tolerable. In this paper, we propose two model editing studies and validate them in the medical domain: (1) directly editing the factual medical knowledge and (2) editing the explanations to facts. Meanwhile, we observed that current model editing methods struggle with the specialization and complexity of medical knowledge. Therefore, we propose MedLaSA, a novel Layer-wise Scalable Adapter strategy for medical model editing. It employs causal tracing to identify the precise location of knowledge in neurons and then introduces scalable adapters into the dense layers of LLMs. These adapters are assigned scaling values based on the corresponding specific knowledge. To evaluate the editing impact, we build two benchmark datasets and introduce a series of challenging and comprehensive metrics. Extensive experiments on medical LLMs demonstrate the editing efficiency of MedLaSA, without affecting irrelevant knowledge that is not edited.