In order to study the scale effect between model and full-scale offshore structures with respect to nonlinear damping force, both free surge/sway decaying tests of a full-scale offshore structure and forced oscillation model tests were carried out. All of the experimental results were evaluated as damping coefficients (drag coefficients) under the assumption that the nonlinear damping force is in proportion to the square of the structure's velocity. A new analysis method, which is based on time series fitting method using a nonlinear optimization technique, is developed and applied for the analysis of free decaying tests. The main results are as follows : 1. The present analysis method is effective to analysis of rapidly decaying data. 2. The drag coefficient can be described as a constant term and a term that is conversely proportional to the Keulegan-Carpenter number, i. e. K_C dependent term. 3. The K_C dependent term in the drag coefficient of a full-scale offshore structure is larger than that of model.