Short Message Service (SMS) is one of the most popular services in the Global System for Mobile (GSM) and many challenges for security arise from the development of message transmission among the broadband network. Recently, an interesting technique called signcryption has been proposed, in which both the properties of signature (ownership) and encryption are simultaneously implemented, with better performance than the traditional signature-then-encryption approach. For the secure mobile computing, we propose a new method for two groups of users that send encrypted signed data by using SMS. We propose a new primitive called verifiable hash convergent group signcryption (VHCGS) by adding the properties of group signcryption and the verification facilities for the third party called the service provider. This research targets toward the type of applications in mobile computing and communication device concerning about SMS.