Recently mobile Stream Control Transmission Protocol (mSCTP) has been proposed as a transport layer approach for supporting mobility. When a mobile terminal (MT) is not located in the home network, a terminal that wishes to communicate with the MT is not able to establish mSCTP association to the MT, since mSCTP does not include the location management mechanism. In order to solve this problem there has been an approach using the Session Initiation Protocol (SIP) INVITE method. However, this approach has shown subsequent delay in acquiring the current location information of the MT when initiating mSCTP association establishment. In this paper, we propose an approach that minimizes the address acquisition delay (AAD) for the applications which does not require multimedia session. The features of proposed approach are follows: (1) SIP request message is not transmitted all the way to MT, but it is only transmitted up until the SIP server which has the current location information of the MT. (2) The final SIP server directly informs the requesting terminal (RT) of the current location information of the MT. The simulation results show that the proposed approach is more efficient than the previous approach in terms of AAD in all kinds of SIP environments.