Multiple autonomous underwater vehicles (Multi-AUVs) cooperative trajectory tracking control is faced with a not fully solved problem of shortening error convergence time while ensuring tracking accuracy. To address this issue, we firstly adopt Newton Raphson Based Optimizer (NRBO) in Nonlinear Model Predictive Control (NMPC) control, and then the leader-follower algorithm is used to make multi-AUVs quickly form a formation to achieve collaborative trajectory tracking. Secondly, utilizing dynamic event triggered when the algorithm convergence speed slows to a certain threshold, the controller is converted from NRBO algorithm to Newton Raphson Broyden Fletcher Goldfarb Shanno (NRBFGS) algorithm. Finally, after optimizing the algorithm, simulation results demonstrate a 40% reduction in trajectory tracking error and a 31% increase in error convergence speed, which indicate that the optimization algorithm proposed in this paper can control multi-AUVs to track the trajectory more quickly and accurately, and significantly improve the performance of multi-AUVs in cooperative trajectory tracking.