Marine seismic surveys are fundamental to seabed topographic mapping and marine resource exploration. As critical components of marine streamer seismic surveys, surface-towed vehicles (STV) require precise straight-line trajectory tracking to ensure the reliability and validity of exploration data. To achieve high-precision tracking for STVs amidst complex marine disturbances, this paper proposes an adaptive super-twisting control (ASTC) method integrated with a novel adaptive law. Firstly, the dynamics of the surface towing system are modeled, where environmental disturbances, parameter uncertainties, and umbilical forces are aggregated into a lumped disturbance term. Subsequently, a trajectory tracking controller is designed based on the proposed ASTC, with the uniform ultimate boundedness of the closed-loop system proven via Lyapunov stability theory. Numerical simulations demonstrate that the method achieves high-precision tracking under various sea states, exhibiting superior robustness. Notably, the proposed strategy effectively mitigates the inherent trade-off between tracking accuracy and control chattering observed in traditional fixed-gain super-twisting control. By dynamically adjusting gains in response to varying disturbances, it ensures superior performance while significantly suppressing chattering.