In public network, user authentication is important security technology. Especially, password-based authentication method is used the most widely in distributed environments, and there are many authentication methods. Their SPMA protocol indicates vulnerability about problem that NSPA protocol does not offer mutual authentication, and proposed Strong Password Mutual Authentication protocol with mutual authentication. However, SPMA protocol has vulnerability of replay attack. In the paper, we analyzed vulnerability to replay attack of SPMA protocol. And we also proposed Improved Strong Password Mutual Authentication protocol to secure on replay attack with same efficiency.