As one of the communication methods in future mobile communications, Machine Type Communication (MTC) is an important mobile communication method in Internet of Things (IoT). When many MTC devices want to access the network at the same time, each MTC device needs to perform independent identity authentication, which will cause network congestion. In order to solve this problem and improve the security of key agreement of MTC device, a dynamic group based effective identity authentication and key agreement scheme was proposed in Long Term Evolution-Advanced (LTE-A) networks. Based on symmetric bivariate polynomials, the proposed scheme was able to authenticate a large number of MTC devices at the same time and establish independent session keys between the devices and the network. In the proposed scheme, multiple group authentications were supported, and the updating of access policies was provided. Compared with the scheme based on linear polynomials, bandwidth analysis shows that the bandwidth consumptions of the proposed scheme during transmission are optimized:the transmission bandwidth between the MTC devices in the Home Network (HN) and the Service Network (SN) is reduced by 132 bit for each group authentication, the transmission bandwidth between the MTC devices within the HN is reduced by 18.2%. Security analysis and experimental results show that the proposed scheme is safe in actual identity authentication and session key establishment, and can effectively avoid signaling congestion in the network.