With the rapid development of mobile networks, there are more and more application scenarios that require group communication. For example, in mobile edge computing, group communication can be used to transmit messages to all group members with minimal resources. The group key directly affects the security of the group communication. Most existing group key agreement protocols are often flawed in performance, scalability, forward or backward secrecy, or single node failure. Therefore, this paper proposes a blockchain-based authentication and dynamic group key agreement protocol. With our protocol, each group member only needs to authenticate its left neighbor once to complete the authentication, which improved authentication efficiency. In addition, our protocol guarantees the forward secrecy of group members after joining the group and the backward secrecy of group members after leaving the group. Based on blockchain technology, we solve the problem of single node failure. Furthermore, we use mathematics to prove the correctness and security of our protocol, and the comparison to related protocols shows that our protocol reduces computation and communication costs.