Since the authentication of digital prescription is a lengthy and error-prone process by pharmacy employees, nowadays in many countries around the world, the paper-based prescription is still the only valid document for patients to purchase their prescribed medication from a pharmacy. Moreover, as a prescription can contain a lot of private information about the patients and their illness, the security and privacy issues in using digital prescription also raise big concerns. Recently, Blockchain has been widely regarded as a promising technology to secure online business data and transactions. In this paper, we present BlockMeds, a Blockchain based online prescription system which enables the authentication of digital prescriptions. Meanwhile, to address the privacy issue during the authentication and transaction for buying the medication, a privacy protection strategy is also implemented in the system. BlockMeds provides the proof of concept for a Blockchain based online prescription system. It also demonstrates the need for privacy protection which is often overlooked in a Blockchain-based system. BlockMeds can be used as a prototype system by both researchers and industrial practitioners who are interested in Blockchain-based medical service systems.