This paper describes the design of a Rudder Roll Damping (RRD) controller based on the linear model of the ship to cope the wave disturbances. A preliminary study of fundamental limitations for linear feedback controllers provides suggestions for the controller design. The RRD is derived using the Internal Model Principle and the optimisation theory. The proposed method directly shapes the output sensitivity function that relates the wave disturbance to ship roll motion. A non-linear constraint optimisation problem is then developed to choose controller parameters in order to make the closed-loop system satisfy specifications and constraints. Numerical results from simulations indicate reasonable roll reduction compared with Minimum Variance Cheap Limiting Optimal Control (MV-CLOC).