This paper proposes a new approach for the design of anti-swing control of overhead cranes. An anti-swing trajectory control scheme is designed based on the trolley and load-hoisting dynamics, and then extended to an adaptive scheme. The load-swing dynamics is controlled by employing a sliding surface that couples the load-swing dynamics with trolley motion. The number of degrees of freedom of the trolley and load-hoisting dynamics is the same as that of the control inputs; therefore, the control problem is reduced to finding a coupled sliding surface that stabilizes the crane control system, based on the load-swing dynamics. In this study, the Lyapunov stability theorem is used as a mathematical design tool. The proposed control guarantees asymptotic stability of the anti-swing trajectory control while keeping all internal signals bounded. The coupled sliding surface allows a direct control of the damping of load swing. In addition, the proposed control provides clear gain-tuning criteria for easy application. Finally, the proposed control realizes an anti-swing control along a typical anti-swing trajectory in practice, with high-speed load hoisting. The validity of the theoretical results is shown by computer simulation.