This paper presents a tagline proportional-derivative control method for suppressing the swing motion of a heavy load suspended by a floating crane in an ocean environment. The tagline mechanism, which is connected between the floating crane and the heavy load, is applied to the floating crane. The winch, which is mounted on the deck of the floating crane, is used to control the tension of the tagline. A proportional-derivative control algorithm is applied to generate the control force of the winch. Swing angle feedback of the proportional-derivative control is supplied by the encoder attached at the boom tip of the floating crane. To demonstrate the performance of the tagline control method, numerical simulations are performed on a non-linear six-dimensional mathematical model of the floating crane and the heavy load. The mathematical model of the floating crane is constructed to consider both the three-degree-of-freedom principle of the floating crane and the heavy load, based on multi-body system dynamics. The numerical and experimental simulation results are compared using a one-hundredth-scale model of the floating crane in the model basin. The results of the numerical simulation and experiment show that the tagline proportional-derivative control method suppresses the swing motion of the load.