This paper mainly focuses on the model-independent multi-target tracking problem of the networked marine surface vehicles (NMSVs) while requiring that the settling time is limited to a predefined one. For addressing such a complex problem, a hierarchical control framework is employed, consisting of a predefined-time distributed estimator (PDE) algorithm and a model-independent predefined-time local tracking (MPLT) algorithm. To be specific, the PDE algorithm aims to estimate the virtual leaders states in a distributed fashion within a predefined time, so that each vehicle obtains its corresponding leaders' information. Based on these estimations, the MPLT algorithm is designed to achieve predefined-time multi-target tracking of the NMSVs. By conducting a rigorous Lyapunov stability analysis, the sufficient conditions guaranteeing the predefined-time stability of the closed-loop system are derived. Subsequently, simulation studies are presented to demonstrate the feasibility and superiority of the proposed approach.