Nonlinear adaptive control of overhead cranes is investigated for anti-sway trajectory tracking with high-speed hoisting motion. The sway dynamics of two dimensional underactuated overhead cranes is heavily coupled with the trolley acceleration, hoisting rope length, and the hoisting velocity which is an obstacle in the design of decoupling control based anti-sway trajectory tracking control law To cope with this obstacle. we propose a fuzzy nonlinear adaptive anti-sway trajectory tracking control law guaranteeing the uniform ultimate boundedness of the sway dynamics even in the presence of uncertainties in such a way that it cancels the effect of the trolley acceleration and hoisting velocity on the sway dynamics. In particular. system uncertainties, including system parameter uncertainty unmodelled dynamics, and external disturbances, are compensated in an adaptive manner by utilizing fuzzy uncertainty observers. Accordingly, the ultimate bound of the tracking errors and the sway angle decrease to zero when the fuzzy approximation errors decrease to zero. Finally, numerical simulations are performed to confirm the effectiveness of the proposed scheme.