The new method which uses the consensus algorithm to solve the coordinate control problems of multiple unmanned underwater vehicles (multi-UUVs) formation in the case of leader-following is adapted.As the communication between the UUVs is difficult and it is easy to be interfered under the water,time delay is assumed to be time-varying during the members communicate with each other.Meanwhile,the state feedback linearization method is used to transfer the nonlinear and coupling model of UUV into double-integrator dynamic.With this simplified double-integrator math model,the UUV formation coordinate control is regarded as consensus problem with time-varying communication delays.In addition,the position and velocity topologies are adapted to reduce the data volume in each data packet which is sent between members in formation.With two independent topologies designed,two cases of communication delay which are same and different are considered and the sufficient conditions are proposed and analyzed.The stability of the multi-UUVs formation is proven by using Lyapunov-Razumikhin theorem.Finally,the simulation results are presented to confirm and illustrate the theoretical results.