Bridge cranes are nonlinear underactuated systems, and the effectiveness of their automatic anti-sway control largely depends on the accuracy of the model. Addressing the underactuation and nonlinearity of these systems significantly increases the complexity of controller design. To reduce the dependency of the anti-sway control system on the dynamic mathematical model of bridge cranes and simplify the design process of the automatic anti-sway controller, a novel control strategy based on the U-model method is proposed. This strategy incorporates an improved iterative learning control algorithm in the design of the U-model-based anti-sway controller, thereby enhancing the response speed of the controller. Simulation and experimental results demonstrate that this control method, while simplifying the modeling and controller design processes, adequately meets the anti-sway requirements of bridge cranes, effectively improving both the response speed and damping precision of the control system.