The Smart home possesses the capability of facilitating home services to their users with the systematic advance in The Internet of Things (IoT) and information and communication technologies (ICT) in recent decades. The home service offered by the smart devices helps the users in utilize maximized level of comfort for the objective of improving life quality. As the user and smart devices communicate through an insecure channel, the smart home environment is prone to security and privacy problems. A secure authentication protocol needs to be established between the smart devices and the user, such that a situation for device authentication can be made feasible in smart home environments. Most of the existing smart home authentication protocols were identified to fail in facilitating a secure mutual authentication and increases the possibility of lunching the attacks of session key disclosure, impersonation and stolen smart device. In this paper, Secure Supervised Learning-based Smart Home Authentication Framework (SSL-SHAF) is proposed as are liable mutual authentication that can be contextually imposed for better security. The formal analysis of the proposed SSL-SHAF confirmed better resistance against session key disclosure, impersonation and stolen smart device attacks. The results of SSL-SHAF confirmed minimized computational costs and security compared to the baseline protocols considered for investigation.