This work aims to get a better insight into the behaviour of CECO, an oscillating-body wave energy converter that presents a singular feature: the motion of its oscillating part is restricted to translations along an inclined axis. In order to study in the time domain the response of CECO for a wide range of wave conditions, a hybrid numerical approach based on the Boundary Element Method (BEM) and the Morison’s equation was used. The effects of the power take-off system were included in the numerical model and calibrated with the results from previous wave basin experiments. The results show that CECO is able to capture up to 40% of the incident wave energy when the direction of translation is 45°. However, if the direction of translation is vertical, the amount of captured wave energy decreases almost three times. This investigation demonstrates the advantage of limiting the oscillation of the CECO floating part to an inclined direction and reaffirms the concept as a promising technology for wave energy conversion.