The ability of a Cycloidal Wave Energy Converter (CycWEC) to cancel irregular deep ocean waves is investigated in a time integrated, inviscid potential flow simulation. A CycWEC consists of one or more hydrofoils attached eccentrically to a shaft that is aligned parallel to the incoming waves. The entire device is fully submerged in operation. A Bretschneider spectrum with 40 discrete components is used to model an irregular wave environment in the simulations. A sensor placed up-wave of the CycWEC measures the incoming wave height and provides a signal for the wave state estimator, a non-causal Hilbert transformation, to estimate the instantaneous frequency, phase and amplitude of the irregular wave pattern. A linear control scheme which proportionally controls hydrofoil pitch and compensates for phase delays is adopted. Efficiency for the design Bretschneider spectrum shows more than 99% efficiency, while non-optimum, off design operating conditions still maintain more than 85% efficiency. These results are in agreement with concurrent experimental results obtained at a 1:300 scale.