There are many semi-submersible offshore structures working in deep waters in the world and many semi-submersible rigs have been built in Japan. Still more, a design of a semi-submersible rig with larger variable deck load has been required and planned for activities in deeper and far waters, and a design condition for a semi-submersible offshore structure has become more severe. Consequently, the importance of a fatigue strength evaluation has been increasing. In this paper, first of all, a fatigue analysis is performed for a semi-submersible rig with 3, 400 tonage variable deck load by a direct calculation method. The direct calculation consists of a motion analysis in regular sine waves, a 3-dimensional frame work analysis and a long-term prediction of stress amplitudes induced in each members of the structure. Subsequently, design wave conditions are proposed for the semi-submersible rig, and the results obtained by the design wave method are compared with the results of the direct calculation. As a result, it is shown that the stress amplitudes calculated for the design wave conditions well correspond to the maximum expected values of stress amplitudes for the probability of 10-8 obtained by the long-term prediction, and the average shape parameter of the longterm distributions of the member stress amplitudes is 1. 1 when Weibull distributions are.applied to.