The secure group communication enables the members, which belong to the same group, to communicate each other in a secure and secret manner. To do so, it is the most important that a group key is securely distributed among them and also group membership is efficiently managed. In detail, the generation, the distribution and the refreshment of a group key would be highly regarded in terms of low communication and computation complexity. In this paper, we show you a new protocol to generate a group key which will be safely shared within a group, utilizing the 2-party Diffie-Hellman key exchange protocol and the complete binary tree. Our protocol has less complexity of computation per group member by substituting many parts of exponentiation computations for multiplications. Consequently, each group member needs constant computations of exponentiation and multiplication regardless of the group size in the protocol and then it has less complexity of the computation than that of any other protocols.