Abstract: The aerial refueling hose is prone to lateral vibration due to external flow fields and platform maneuvering, which can develop into a whipping phenomenon in severe cases. This complex dynamic behavior, governed by the dynamic characteristics of distributed parameter systems, poses significant challenges to the boundary stabilization control of the hose system and seriously endangers the safety of the aerial docking process. This paper investigates the vibration suppression and boundary stabilization problems of a flexible aerial refueling hose subjected to aerodynamic disturbances by introducing a cleverly designed super-twisting sliding mode control framework. Based on the principle of virtual work, a set of partial differential equations and the associated boundary conditions for the flexible aerial refueling hose are established. By integrating the super-twisting algorithm with a barrier function-based disturbance observer, an innovative finite-time sliding mode controller is proposed. The stability and convergence of the closed-loop system are rigorously proven using Lyapunov theory. Numerical simulation results demonstrate that the proposed control method effectively eliminates hose vibrations. Under constant-velocity motion conditions, the root mean square value of the displacement at the hose tip (x = L) is 0.1672, representing a reduction of approximately 95.3% compared to 3.5264 achieved by an existing boundary control method. At the midpoint of the hose (x = L/2), the root mean square value of the displacement is 1.0063, which is reduced by approximately 17.3% compared to 1.2164 achieved by the proportional-integral-derivative (PID) control method and by approximately 59.5% compared to 2.4857 achieved by the existing boundary control method. Superior vibration suppression performance is thus achieved at different positions along the hose. This study provides a high-performance alternative to PID control, backstepping control, and their derivative methods for distributed parameter systems such as hose-type partial differential equation systems.