The main concern in mobile peer-to-peer (P2P) networks is security because jamming or eavesdropping on a wireless link is much easier than on a wired one and such damage can be incurred without physical access or contact. In particular, authentication has increasingly become a requirement in mobile P2P environments. This paper presents a new mutual authentication mechanism which requires less storage space and maintains a high level of security in mobile P2P networks. The proposed mechanism improves efficiency by avoiding the use of centralized entities and is designed to be agile in terms of both reliability and low-cost implementation. The mechanism suggested in the simulation evaluates the function costs occurring in authentication between the devices under mobile P2P network environment comparing to existing method in terms of basic operation costs, traffic costs, communications costs, storage costs and scalability. The simulation results show that the proposed mechanism provides high authentication with low cryptography processing overhead.