This paper presents the design and simulation testing of a control law for autonomous recovery of a rotorcraft to a moving ship. The paper focuses on the final approach, descent, and landing phases of the ship recovery task when the flight deck is moving dynamically due to sea state. The controller design is based on the dynamic inversion method, and it is assumed that the inertial position of the flight deck is measured and available to the controller. The controller is tested and demonstrated using a FLIGHTLAB simulation model of a medium utility helicopter operating on a ship similar to a DDG-51 destroyer. The decelerating approach profile is based on profiles typically used by human pilots. Two different methods are investigated for the landing: 1) deck tracking with a steady decrease in height above deck, and 2) an optimal control approach that uses forecasted deck state as the terminal condition. Deck motion prediction is achieved via a Minor Components Analysis algorithm that uses recorded state history of the deck motion to predict deck state five seconds in the future. Simulation results show the controller performs well in tracking the straight and oblique approach paths, but its performance can be sensitive to path parameters that result in aggressive deceleration. The simple deck tracking approach to landing resulted in surprisingly good performance when tested over 30 randomized cases, but this control strategy results in large amplitude maneuvering in lateral and vertical axes throughout the descent. The predictive landing method showed potential for achieving more efficient landings with less maneuvering, but overall controller performance was less consistent and sensitive to inaccuracies in the deck motion prediction. The deck motion prediction and optimal control methods require further development to provide reliable autonomous landings.