For a turret-moored Floating Liquefied Natural Gas Plant (FLNG), it is important to use confidently derived low frequency viscous damping coefficients in the prediction of its motions and mooring loads in wind, wave and current conditions. In this paper we present our recent experimental work on the low frequency sway and yaw viscous damping in calm water and in current. In general, damping force is a relatively small portion of the total hydrodynamic force on an oscillatory model. In a previous ExxonMobil damping test in calm water (Huang et al., 2010), i.e. without current and wave, a deeply submerged double-body model was forced to oscillate to avoid surface wave contamination. An inertia compensation system was also designed to cancel the inertia force and the restoring force during oscillations, then the measured force was mainly damping force. Because of the schedule constraints of the present study, it was not possible to perform the submerged oscillation test. Instead, a forced oscillation test in water surface was performed based on KC-number and β-number. In order to obtain reliable damping coefficients, we had to carefully design the test conditions, i.e. current speeds, oscillation amplitudes and frequencies so that an adequate portion of damping force within the total force could be achieved with no significant surface waves that could contaminate the damping results being generated by the oscillating model. Good damping results were obtained. To check the acceptance of the test method based on Froude scaling, a limited number of tests were performed in which the oscillation amplitudes and frequencies were scaled down based on the Froude scaling. Magnitudes of the measured force and moment are significantly low. The time series of the measurements have drifting and significant noise. We could not confidently determine viscous damping results from the measurements.