The non-linear viscous damping forces on a Tension Leg Platform (TLP) column experiencing "springing" vibration are calculated by directly solving the Navier–Stokes equations. Different characteristics of heave damping have been found in two different regimes in the ranges of Keulegan–Carpenter (KC) from 0.001 to 1.0 and β from 89 236 to 435 298. At very low KC, the heave damping force tends to be approximately linear with the velocity, whereas a definite non-linear dependence on the velocity has been found as KC increases. It is found that the laminar boundary layer theory based on the infinite length circular cylinder assumption is still suitable to the friction drag estimation at very low KC, but the leading edge effect is not negligible as KC approaches 2π/(D/Td) (D=diameter of the cylinder, and Td=the draft of the cylinder). From the present numerical estimation, one can conclude that a uniform scaling law cannot be applied, and the scaling laws for the heave damping estimation of a TLP column in two different regimes have been presented.