Considering the problem of AUV formation cooperative control in underwater acoustic communication with random time delay, this paper proposes a distributed model prediction based AUV formation control method. Firstly, the asynchronous state information is transformed into synchronous state information by the designed random time-delay communication synchronization strategy, and then the cooperative formation cost function is described by combining virtual trajectory, state prediction, control constraints and AUV state information. The formation control function is introduced into local rolling time domain optimization to achieve formation control objectives. The Lyapunov theory is used to prove the stability of formation controller. Finally, the proposed method is compared with the existing formation control methods, and the results verify its effectiveness.