It is often desirable to keep the load of an offshore crane in a fixed point in space despite the movement of its base. To solve the problem of stabilizing the load’s position, the authors have proposed application of the hoisting winch drum’s drive and an auxiliary system. The auxiliary system enables independent moving of a selected point of the hoisting rope in two perpendicular planes. In this paper, two methods for determining the drive functions of the auxiliary system and the hoisting winch’s drum ensuring stabilization of an offshore crane’s load are presented. Both methods are based on a simplified model of a crane and allow compensation for a pseudo-harmonic base motion. In order to take into account the deviations of base motion from the assumed and avoid over simplifications, the second, more sophisticated model is developed. This model is proposed to be applied in closed-loop control systems with a PID controller. Results of sample numerical simulations are included that proved useful information about the developed methods and models for stabilization of an offshore crane’s load.