Designing an autonomous precise controller for ships requires accurate and reliable ship models, including the ship dynamic model and actuator model. However, selecting a suitable model for controller design and determining its parameters pose a significant challenge, considering factors such as ship actuation, input constraints, environmental disturbances, and others. This challenge is further amplified for underactuated ships, as obtaining decoupled experiment data is not feasible, and the limited data available may not adequately represent the motion characteristics of ships. To address this issue, we propose a novel model-based parameter estimation approach, called MBPE-LOGO, for underactuated ship motion models. This method combines local optimization and global optimization methods to solve the model identification problem using a dataset generated from real experiments. The effectiveness of the identified model is verified through extensive comparisons of different trajectories and prediction steps.