With the rapid advancement of deep learning, particularly in the field of medical image analysis, an increasing number of Vision-Language Models (VLMs) are being widely applied to solve complex health and biomedical challenges. However, existing research has primarily focused on specific tasks or single modalities, which limits their applicability and generalization across diverse medical scenarios. To address this challenge, we propose UMIT, a unified multi-modal, multi-task VLM designed specifically for medical imaging tasks. UMIT is able to solve various tasks, including visual question answering, disease detection, and medical report generation. In addition, it is applicable to multiple imaging modalities (e.g., X-ray, CT and PET), covering a wide range of applications from basic diagnostics to complex lesion analysis. Moreover, UMIT supports both English and Chinese, expanding its applicability globally and ensuring accessibility to healthcare services in different linguistic contexts. To enhance the model's adaptability and task-handling capability, we design a unique two-stage training strategy and fine-tune UMIT with designed instruction templates. Through extensive empirical evaluation, UMIT outperforms previous methods in five tasks across multiple datasets. The performance of UMIT indicates that it can significantly enhance diagnostic accuracy and workflow efficiency, thus providing effective solutions for medical imaging applications.