The natural ocean/river currents energy can be harvested using Flow Induced Motion (FIM) phenomena. The effect of damping-ratio and mass-ratio on Flow Induced Motion energy harnessing of a square cylinder are numerically investigated for Reynolds number 15500 < Re < 232000 (0.2 m/s < flow velocity < 3.0 m/s). Four typical regions can be observed in the Flow Induced Motion responses, including Vortex Induced Vibration (VIV) Initial Branch, Vortex Induced Vibration Upper Branch, Vortex Induced Vibration-Galloping Transition and Galloping. Results indicate that as the velocity increases, the number of vortices shed per cycle increases, and the harnessed power increases without upper limit. The energy conversion efficiency increases up to the highest value until the Vortex Induced Vibration upper branch. Then, it starts decreasing and tends to a relatively small value in the galloping region. Increasing mass ratio will shorten the velocity range of Vortex Induced Vibration. High damping-ratio has a negative impact on oscillation amplitude, but provides a boost for energy harnessing. In all tests, the power (143 W) is considerable at damping-ratio = 0.6. As the damping-ratio reaches up to 0.8 (nearing critical damping), galloping will no longer occur. (C) 2017 Elsevier Ltd. All rights reserved.