A double-skinned composite tubular (DSCT) offshore wind power tower was designed. Because a heavy wind power turbine is supported by a slender tower, the actual resisting moment capacity of the tower against wind load becomes less than its original moment capacity as its lateral displacement increases. Therefore, its actual moment capacity should be found for safe design by considering large displacement effect. In this study, 40 sections of DSCT wind power towers were designed for a 5.0MW turbine and the performances of the designed 40 sections were analyzed with and without considerations of large displacement effect. In designing and analyzing them, the material nonlinearity and the confining effect of concrete considered. The comparison of the analysis results showed the moment capacity loss of the wind power tower by the mass of the turbine is significant and the large displacement effect should be considered for the safe design of the wind power tower.