Abstract: In order to solve the technical problem of real-time dynamic tracking of underwater moving targets for autonomous underwater vehicle (AUV), an iterative optimization algorithm is proposed, which combines the fading memory recursive least square (FMRLS) algorithm with the square root algorithm.It makes full use of the fast convergence performance of FMRLS algorithm, and uses the square root algorithm to solve the numerical instability problem in the iterative process.The iterative optimization algorithm can quickly calculate the initial distance, the heading angle and the moving direction of the moving target, and the numerical convergence time is about 3 min, as well as the target moving speed can be converged in about 5 min.With the proposed algorithm, the converge time is short, the computing velocity is high, and moreover, an AUV can keep hovering without any form of maneuverer from itself.Those advantages of the proposed algorithm make it a perfect solution for practical engineering problems of underwater moving target tracking.