To increase the amount of energy captured from a vibrating buoy in the ocean with a simple mechanism, this paper proposes a two-body point absorber wave energy converter (WEC) with a tuned inerter. The tuned inerter mechanism consists of a spring, a linear damping element, and a component called inerter. This mechanism was originally proposed in the field of civil engineering as a structural control device which can absorb energy from vibrating structures effectively by taking advantage of the resonance effect of the inerter part. In addition to this mechanism where a generator is used as the linear damping element, the current of the generator for the power take-off system is controlled based on the algorithms proposed in literature to achieve further improvement of the power generation capability. In this research, a detailed analytical model of the proposed WEC is introduced and developed. Then the power generation performances of full-scale WEC models are assessed through numerical simulation studies using WAMIT software and it is shown that the current-controlled WEC with the proposed mechanism achieves an 88% increase compared to the conventional one for the JONSWAP spectrum with 6 s peak period and 1 m significant wave height.