In this paper, we aim to develop an open-source, multilingual language model for medicine, that the benefits a wider, linguistically diverse audience from different regions. In general, we present the contribution from the following aspects: first, for multilingual medical-specific adaptation, we construct a new multilingual medical corpus, that contains approximately 25.5B tokens encompassing 6 main languages, termed as MMedC, that enables auto-regressive training for existing general LLMs. second, to monitor the development of multilingual LLMs in medicine, we propose a new multilingual medical multi-choice question-answering benchmark with rationale, termed as MMedBench; third, we have assessed a number of popular, opensource large language models (LLMs) on our benchmark, along with those further auto-regressive trained on MMedC, as a result, our final model, termed as MMedLM 2, with only 7B parameters, achieves superior performance compared to all other open-source models, even rivaling GPT-4 on MMedBench. We will make the resources publicly available, including code, model weights, and datasets.