Wearable devices are used in various applications to collect information including step information, sleeping cycles, workout statistics, and health-related information. Due to the nature and richness of the data collected by such devices, it is important to ensure the security of the collected data. This paper presents a new lightweight authentication scheme suitable for wearable device deployment. The scheme allows a user to mutually authenticate his/her wearable device(s) and the mobile terminal (e.g., Android and iOS device) and establish a session key among these devices (worn and carried by the same user) for secure communication between the wearable device and the mobile terminal. The security of the proposed scheme is then demonstrated through the broadly accepted real-or-random model, as well as using the popular formal security verification tool, known as the Automated validation of Internet security protocols and applications. Finally, we present a comparative summary of the proposed scheme in terms of the overheads such as computation and communication costs, security and functionality features of the proposed scheme and related schemes, and also the evaluation findings from the NS2 simulation.