In this paper, we propose a USIM-based Authentication Scheme for 3GPP Network Access. The proposed scheme improves the problems of existing authentication protocol in 3GPP Network such as sequence number synchronization problem, the storage overhead of authentication data, and bandwidth consumption between Serving Network and Home Network. Our proposal is based on the USIM-based Authentication and Key Agreement Protocol that is defined in 3GPP Specification. In our scheme, mobile nodes share a SK with Serving Network and use a time stamp when mobile nodes are performing an authentication procedure with Serving Network. By using time stamp, there is no reason for using sequence number to match the authentication vector between mobile nodes and networks. So, synchronization problem can be solved in our scheme. As well as our scheme uses an authentication vector, the storage overhead of authentication data in Serving Network and bandwidth consumption between networks can be improved.