This paper investigates the model-free cluster formation problem of the networked marine surface vehicles facing the cases of external disturbances and bounded inputs constraint. To handle such a complex problem, a predefined-time estimator-based hierarchical control algorithm is designed in a bounded way and without prior model information, which then decomposes the aforementioned problem into two subcontrol problems, namely, the distributed predefined-time estimation problem and the local tracking problem. Specifically, a novel distributed predefined-time estimator algorithm is designed such that the states of the virtual leaders can be estimated by their corresponding follower vehicles within a predefined time. Further, these obtained estimators are employed to construct the local bounded model-free tracking controller to finally address the considered problem. The sufficient conditions for solving these two subcontrol problems by using the designed algorithm are derived based on systematic and thorough Lyapunov stability analysis. Finally, digital simulation experiment on the networked Cyber-Ships II are carried out to verify the main results.