Internet of Things (IoT) devices pose significant security challenges due to their heterogeneity (i.e., hardware and software) and vulnerability to extensive attack surfaces. Today's conventional perimeter-based systems use credential-based authentication (e.g., username/password, certificates, etc.) to decide whether an actor can access a network. However, the verification process occurs only at the system's perimeter because most IoT devices lack robust security measures due to their limited hardware and software capabilities, making them highly vulnerable. Therefore, this paper proposes a novel approach based on Zero Trust Architecture (ZTA) extended with blockchain to further enhance security. The blockchain component serves as an immutable database for storing users' requests and is used to verify trustworthiness by analyzing and identifying potentially malicious user activities. We discuss the framework, processes of the approach, and the experiments carried out on a testbed to validate its feasibility and applicability in the smart city context. Lastly, the evaluation focuses on non-functional properties such as performance, scalability, and complexity.