In recent years, blockchain-related technologies and applications have gradually emerged. Blockchain technology is essentially a decentralized database maintained by the collective, and it is now widely applied in various fields. At the same time, with the development of medical technology, medical information is becoming increasingly important in monitoring the patient’s medical examination and treatment process. Medical information must be the most private information about a person. However, due to issues such as operation errors within the network or a hacking attack by a malicious person, there have been major leaks of sensitive personal information. Therefore, it is an issue worth studying to ensure patients’ privacy and protect these medical materials. On the other hand, the patient’s Electronic Medical Record (EMR) cannot be searched across the hospital under the current medical system. As a result, repeated examinations can occur when the patient attends the hospital for treatment, resulting in a waste of medical resources. This study has deployed Blockchain to store and share Electronic Medical Records in a transparent and non-repudiation manner. In addition, we evaluated and tested the proposed system with various test cases and examined the performance with various numbers of transactions. Moreover, we have deployed Symmetric and Asymmetric key cryptography to exchange and share patients’ Electronic Medical Records. The proposed system is expected to provide an interesting solution for exchanging medical data between medical facilities, especially for hospital transfers in Vietnam.