On the basis of a time-domain HOBEM (higher-order boundary element method), a two-dimensional (2D) fully nonlinear numerical model is developed to investigate the wave energy capturing efficiency of an OWSC (oscillating wave surge converter) in the presence of uniform currents. In the model, the wave energy is extracted through a linear external damping coefficient, and the natural frequency of the OWSC is tuned to the wave characteristics by introducing an elastic and inertia coefficient. On the free surface, a five-point fourth order Lagrangian interpolation method is applied to determine the redistribution of meshes, and a rotation scheme of spatial coordinate system is employed to tackle the discontinuity of flux at the intersection points. The wave loads on the wetted body surface are then evaluated using two auxiliary functions through which the mutual dependence of body motion and fluid flow is decoupled. The present model is validated against the published experimental and numerical results for an OWSC in large motion excited by nonlinear waves. Simulations are performed to capture the hydrodynamic behavior of the OWSC with different currents. Numerical results are also provided to show the behavior dependence on the design parameters, such as current velocities, wave conditions, geometric characteristics and mechanical properties.