The motion response of a shear-leg crane ship lifting a heavy load in wave groups was investigated. The 9-DOF dynamic model incorporated hull motions coupled with nonlinear large-angle load swing and elastic stretch of the hoisting rope assembly. Hydrodynamic response forces and wave excitation forces were taken to be frequency dependent, and nonlinear mooring system restoring forces were allowed for. Closed-form linearized results about the system equilibrium state verified our nonlinear simulation algorithm; simulation results in comparison with scale model test measurements, our mathematical model. Wave groups were idealized in two different ways: 1) as continuous wave groups produced by pairs of beating waves of equal amplitude and slightly different periods, and 2) as isolated wave packets generated by superimposing a large number of regular wave components derived from a Gauss-modulated amplitude spectrum. Simulations show that hook load response, strongly coupled with ship motions, was mainly influenced by first-order wave-exciting forces. Low-frequency horizontal ship motions caused by second-order wave (drift) forces did not generally affect hook load response, i.e., first-order and second-order responses were independent.