The mobile Virtual Private Network (MVPN) of Internet Engineering Task Force (IETF) is not designed to support NEwork MObility (NEMO) and is not suitable for real-time applications. Therefore, an architecture and protocol which supports VPN in NEMO are needed. In this paper, we proposed the cost-reduced secure mobility management scheme (CR-SeMMS) which is designed for real-time applications in conjunction with VPN and also which is based on the session initiation protocol (SIP). Our scheme is to support MVPN in NEMO, so that the session is well maintained while the entire network is moved. Further, in order to reduce the authentication delay time which considers as a delaying factor in hands-off operations, the signaling time which occurs to maintain the session is shortened through proposing the hands-off scheme adopting an authentication method based on HMAC based One Time Password (HOTP). Finally, our simulation results show the improvement of the average hands-off performance time between our proposed scheme and the existing schemes.