In this paper, a new nonlinear dynamic model is derived for a 2-dimensional overhead crane based on a new definition of 2-degree-of-freedom swing angle, and a new anti-swing control law is proposed for the crane. The dynamic model and control law take simultaneous travel and traverse motions of the crane into consideration. The model is first linearized for small motions of the crane load about the vertical stable equilibrium. Then the model becomes decoupled and symmetric with respect to the travel and traverse axes of the crane. From this result, a decoupled anti-swing control law is proposed based on the linearized model via the loop shaping and root locus methods. This decoupled method guarantees not only fast damping of load-swing but also zero steady state position error with optimal transient response for the 2-dimensional motion of the crane. Finally, the proposed control method is evaluated by controlling the simultaneous travel and traverse motions of a 2-dimensional prototype overhead crane. The effectiveness of the proposed control method is then proven by the experimental results.