Two-degree-of-freedom (2DOF) fully passive motion of a flapping foil at a low Reynolds number Re = 10,000 is studied numerically. The simulations are conducted using open source computational fluid dynamics (CFD) toolbox OpenFOAM. The present research is mainly focused on the self-sustained limit-cycle oscillations of a flapping foil with potential application as a hydro-energy harvester. The effect of different parameters on the onset of linear flutter, the characteristics of the system response, the available power from a flapping foil and the flow patterns are investigated. It is found that given a small initial perturbation, the response of the foil is similar to that of classical linear flutter i.e., the oscillations converged to a constant value at reduced velocities lower than the flutter velocity and limit-cycle oscillations (LCOs) are observed once the reduced velocities are greater than the flutter velocity. The reduced frequency of the LCOs exhibits a decreasing trend with increasing reduced velocity. In contrast, the phase difference between pitch and plunge increases with the increase of the reduced velocity. The feasibility of power extraction is demonstrated and the time-averaged power shows a single peak at an intermediate reduced velocity. Limit-cycle oscillations are found to be influenced by leading-edge vortex shedding as well as trailing-edge flow separation.