This paper deals with optimal tuning, control and performance evaluation of an inerter-based point absorber (IPA) wave energy converter (WEC), which is a first step towards establishing an integrated offshore wind-wave energy system. An inerter–spring system is introduced into a conventional WEC, which can improve the system performance when properly tuned and controlled. Analytical expressions of the optimal IPA parameters have been derived under regular waves. Closed-form solution of the capture width ratio of the IPA under optimal control is obtained and verified by the theoretically optimal solution of a point absorber. Next, hybrid and passive control strategies for the IPA are also investigated, demonstrating superior energy absorption performance than the conventional point absorber under the same control strategy, due to the existence of an extra resonance and amplified motion of the inerter. Furthermore, the performance of passive IPA is evaluated under irregular waves, where parametric optimization has been performed with constraints on system modal frequencies. Single-mode and double-mode resonances have been observed for wave peak frequencies away from and close to the float natural frequency, respectively. This facilitates the frequency adaption of the IPA and the resulting superior performance in terms of more energy absorption and broader operational bandwidth.