With the pervasiveness of the Internet of Things (IoT) and the rapid progress of wireless communications, Wireless Body Area Networks (WBANs) have attracted significant interest from the research community in recent years. As a promising networking paradigm, it is adopted to improve the healthcare services and create a highly reliable ubiquitous healthcare system. However, the flourish of WBANs still faces many challenges related to security and privacy preserving. In such pervasive environment where the context conditions dynamically and frequently change, context-aware solutions are needed to satisfy the users' changing needs. Therefore, it is essential to design an adaptive access control scheme that can simultaneously authorize and authenticate users while considering the dynamic context changes. In this paper, we propose a context-aware access control and anonymous authentication approach based on a secure and efficient Hybrid Certificateless Signcryption (H-CLSC) scheme. The proposed scheme combines the merits of Ciphertext-Policy Attribute-Based Signcryption (CP-ABSC) and Identity-Based Broadcast Signcryption (IBBSC) in order to satisfy the security requirements and provide an adaptive contextual privacy. From a security perspective, it achieves confidentiality, integrity, anonymity, context-aware privacy, public verifiability, and ciphertext authenticity. Moreover, the key escrow and public key certificate problems are solved through this mechanism. Performance analysis demonstrates the efficiency and the effectiveness of the proposed scheme compared to benchmark schemes in terms of functional security, storage, communication and computational cost.