Abstract: Gives an approach for the design of a controller for under-actuated overhead crane systems for simultaneously achieving the objectives of precise displacement tracing and anti-swing.Considering some uncertainties of two degrees of freedom(TDOF)overhead crane systems,such as payload variation and disturbances,a cascade sliding mode direct adaptive fuzzy controller is designed based on Lyapunov function method and fuzzy logical systems(FLS).It was proved by theoretical analysis and simulations that the uncertain crane control systems were global asymptotically stable,and had good adaptability and robustness.