In peer-to-peer environment, information is directly exchanged between nodes instead of forwarding by a central server, hence user-to-user authentication becomes a critical security issue in such environment. Existing solutions are based on public-key cryptosystem. The main concerns in a public-key cryptosystem include authenticity of the public key and lack of efficiency. A trusted third party is also involved in a public-key environment. This paper proposed an efficient one-way hash function based user-to-user authentication scheme with smart card in peer-to-peer system. In the proposed scheme, the system and peers do not have to maintain verification tables, and a trusted third party is not needed in the run time. The proposed scheme achieves mutual authentication at very low computational cost, but also provides good security strength.