Secure group communication is an important research issue in the field of cryptography and network security, because group applications like online chatting programs, video conferencing, distributed database, online games etc. are expanding rapidly. Group key agreement protocols allow that all the members agree on the same group key, for secure group communication, and the basic security criteria must be hold. The design of secure group communication can be very critical for achieving security goals. Many group key agreement protocols such as Tree-based Group Diffie-Hellman (TGDH) Kim et al. (ACM Trans Inf SystSecur (TISSEC) 7(1): 60-96, (2004)) [1], Group Diffie-Hellman (GDH) Steiner et al. (IEEE TransParallel Distrib Syst 11(8): 769-780, (2000)) [2], Skinny Tree (STR) Wong et al. (IEEE/ACMTrans Netw 8(1): 16-30, (2000)) [3] etc., have been established for secure group communication, but they have suffered from unnecessary delays as well as their communication cost increased due to increased exponentiation. An alternative approach to group key agreement is the queue based group key agreement protocol that reduces unnecessary delays, considers member diversity with filtering out low performance members in group key generation processes. We propose a novel queue based group key agreement protocol that uses the concepts of elliptic curve cryptography. The proposed protocol gives better results than the other existing related protocols and it also reduces computational overheads.