A new concept of power generator using self-induced oscillating hydrofoil with upwind arm and downwind arm configurations to extract energy from fluid is proposed and numerically tested in the present study. The pitching motion of the symmetrical hydrofoil with camber is induced by the shedding vortexes downward the hydrofoil, and a pitching damper with critical pitching angle is utilized to control the pitching amplitude. Two-dimensional Navier-Stokes simulation at Re = 1100 are carried out to study the fluid-hydrofoil interaction as well as the performance of energy extraction. The effects of camber, critical pitching angle, arm length and swing direction are systematically studied. Numerical results demonstrate that camber and critical pitching angle have significant effects on the energy extraction performance of the power generator, and optimized camber and critical pitching angle configurations can increase the power coefficient and efficiency dramatically. With best structural parameters and hydrofoil shape, the power generator can reach maximum power coefficient of 0.8 and energy extraction efficiency of 0.285. Besides, the upwind arm configuration achieves better performance over the downwind arm configuration. The effect of arm length is not so profound as other parameters in our study.