For the security flaws in 3G authentication and key agreement(3GPP AKA) protocol,an efficient and robust authentication and key agreement(ER AKA) protocol is proposed,thus to prevent the redirection attack,and the active attack based on the corrupted network,the defect of SQN synchronization and the leakage of users' identity information.Then the safety and efficiency of ER AKA is analyzed,and the analysis shows that ER AKA could solve the security problems at the cost of fairly few storage resource and computing resources,and reduce signaling overhead.