There is an intuitive connection between signcryption and key agreement. Such a connector may lead to a novel way to construct authenticated and efficient group key agreement protocols. In this paper, we present a primary approach for constructing an authenticated group key agreement protocol from signcryption. This approach introduces desired properties to group key agreement. What this means is that the signcryption gives assurance to a sender that the key is available only to the recipient, and assurance to the recipient that the key indeed comes from the sender. Following the generic construction, we instantiate a distributed two-round group key agreement protocol based on signcryption scheme given by Dent [8]. We also show that this concrete protocol is secure in the outsider unforgeability notion and the outsider confidentiality notion assuming hardness of the Gap Diffie-Hellman problem.