There has been tremendous growth in the application of the Internet of Things (IoT) in our daily lives. Yet with this growth has come numerous security concerns and privacy challenges for both the users and the systems. Smart devices have many uses in a healthcare system, e.g. collecting and reporting patient data and controlling the administration of treatment. In this paper, we address the specific security issue of access control for smart healthcare systems and the protection of smart things from unauthorised access in such large scale systems. Commonly used access control approaches e.g. Role-Based Access Control (RBAC), AttributeBased Access Control (ABAC) and Capability-Based Access Control (CapBAC) do not, in isolation, provide a complete solution for securing access to IoT-enabled smart healthcare devices. They may, for example, require an overly-centralised solution or an unmanageably large policy base. We propose a novel access control architecture which improves policy management by reducing the required number of authentication policies in a large-scale healthcare system while providing fine-grained access control. The devised access control model employs attributes, roles and capabilities. We apply attributes for role membership assignment and in permission evaluation. Membership of roles grants capabilities. The capabilities which are issued may be parameterised based on attributes of the user and are then used to access specific services provided by things. We also provide a formal specification of the model and a description of its implementation and demonstrate its application through different use-case scenarios. The evaluation results of core functionality of our architecture are provided with the practical testbed experiments.