Modern marine systems analysis and design usually require to have an accurate representation of its mathematical models to reflect the changing environmental conditions and the complexity of the external infrastructure. To obtain such models, we need to carry out experimental tests for various regimes of motion. There exist a wide number of techniques to define mathematical models on the base of experimental data. This paper is devoted to neural network approach for parametric identification of a linear mathematical model for a surface vessel under external disturbance action. Training data for the proposed method are based on information about the state space vector and its derivative. L1-filtering is used for the training set preprocessing to increase parameters estimation performance. The static neural network is training for approximation the right side function of the mathematical model describing vessel dynamic. Estimates for model parameters are obtained by neural network linearization.