In IP Multimedia Subsystem (IMS) of UMTS, both packet-switch domain and IMS authentications are necessary for the IMS subscriber, so-called the two-pass authentication. However, the IMS authentication is carried out by IMS authentication and key agreement (IMS AKA). Since IMS AKA is based on 3GPP AKA that is used to Packetswitch domain authentication, almost all of the operations are the same. It is inefficient that almost all involved steps in the two-pass authentication are duplicated. Hence, Lin et al's proposed the one-pass authentication to increase efficiency of the IMS authentication. Unfortunately, in addition to some security problems, the one-pass authentication procedure only has unilateral authentication without capabilities of mutual authentication and key agreement. Therefore, this paper proposes an one-pass AKA procedure, which not only avoids the lacks of the one-pass authentication procedure but also does not lose the efficiency.