A differential drive catamaran unmanned surface vehicle tracking control in presence of external disturbances and uncertainties is addressed. A super-twisting control considering a single adaptive gain is adopted, where the number of tuning parameters of this control gain is reduced compared with standard adaptive super-twisting approaches. Furthermore, the gain exhibits smooth dynamics compared with controls using discontinuous functions signals. An analysis of the closed loop stability is provided using a Lyapunov approach. The proposed adaptive super-twisting approach is designed to drive the vessel along time-varying trajectories in presence of perturbations, ensuring robustness, and practical finite-time convergence. Numerical simulations, and real-time experimental tests using a prototype, illustrate the control performance under payload uncertainty and external perturbations. For further demonstration, a comparison with some of the existing versions of the super-twisting control included one with variable gain is provided.