To solve the problem of Autonomous underwater vehicle (AUV) formation cooperative control in complex Marine environment, a robust model predictive control strategy based on adaptive measure-communication framework is proposed in this paper. This method can avoid the delay and packet loss of the explicit communication interaction mode based on underwater acoustic broadcast under complex underwater conditions. Firstly, an adaptive measures-communication framework is proposed, which uses non-explicit communication to observe the internal state of the formation and introduces an adaptive Kalman filter to compensate for external disturbances in the measures-communication link. Secondly, a distributed robust model predictive controller is designed based on the auxiliary control law to realize the AUV formation tracking control under multi-condition constraints. The stability of the AUV formation controller is proved by the Hamilton function and terminal constraint theory. Finally, the simulation results of 5 AUVs in different scenarios are compared and analyzed to verify the effectiveness of the proposed method.