The space-ground integrated network has the characteristics of open communication link, narrow bandwidth and limited satellite computing resources. Aiming at the problem that the existing authentication and key agreement (AKA) protocol can not meet the communication scenario of the space-ground integrated network, this paper analyzes the security performance requirements of the space-ground integrated network, and proposes a networking AKA protocol, including two stages of adjacent node networking AKA and cross-node networking AKA. In the phase of adjacent node networking AKA, the networking AKA are performed based on the ground AAS to generate inter-satellite authentication credentials. In the cross-node networking AKA stage, based on the authentication credentials generated by adjacent satellite authentication, the Chebyshev chaotic mapping technology is used to realize cross-node inter-satellite mutual authentication. Security and performance analysis show that our protocol has certain advantages in security, and improves the computation and communication efficiency to meet the lightweight requirements of the space-ground integrated network.