A bridge crane is a complicated nonlinear underactuated mechatronic system, for which high-speed positioning and anti-swing control is the kernel objective. Existing methods for varying cable length cranes require either linearizations or approximations, when performing analysis, and they usually assume small load swing; moreover, the ranges of the tracking errors cannot be guaranteed during the overall process. Motivated by these facts, we present a new tracking scheme for cranes with load horizontal transportation and lowering control, which achieves simultaneous load swing suppression and elimination. To the best of our knowledge, the proposed method yields the first feedback closed-loop control result not needing linearization or approximation operations to the original nonlinear crane dynamics with cable length variation, while relaxing the common assumption imposed on load swing associated with existing methods. It can also guarantee that the tracking errors are always within a priori set bounds and converge to zero rapidly. Lyapunov-like analysis is implemented to support the theoretical derivations. We carry out hardware experiments to illustrate the superior control performance of the new method. (C) 2014 Elsevier Ltd. All rights reserved.