A drogue is used to stabilise and straighten seismic arrays so that seismic waves can be well-received. To embed the effect of a cone-shaped drogue into the numerical modelling of the deep-towed seismic survey system, one surrogate model that maps the relationship between the hydrodynamic characteristics of the drogue and towing conditions was obtained based on data-driven simulations. The sample data were obtained by co-simulation of the commercial software RecurDyn and Particleworks, and the modelling parameters were verified by physical experiments. According to the Morison formula, the rotational angle, angular velocity, angular acceleration, towing speed, and towing acceleration of the drogue were selected as the design variables and drag forces and aligning torque were selected as the research objectives. The sample data of more than 8500 sets were obtained from virtual manoeuvres. Subsequently, both polynomial and neural network regression algorithms were used to study these data. Finally, analysis results show that the surrogate model obtained by machine learning has good performance in predicting research objectives. The results also reveal that the neural network regression algorithm is superior to the polynomial regression algorithm, its largest error of mean square is less than 0.8 (N²/N² mm²), and its R-squared is close to 1.