This paper proposes an anonymity based mechanism for providing privacy in IoT environment. Proposed scheme allows IoT entities to anonymously interacting and authenticating with each other, or even proving that they have trustworthy relationship without disclosing their identities. Authentication is based on an anonymous certificates mechanism where interacting IoT entities could unlinkably prove possession of a valid certificate without revealing any incorporated identity-related information, thereby preserving their privacy and thwarting tracking and profiling attacks. Through a security analysis, we demonstrate the reliability of our solution.