Many case histories of re-liquefaction phenomena seem to support the idea that sand deposits, if they once have been liquefied, could be reliquefied again by a subsequent earthquake even though the earthquake is smaller than the previous one. The magnitude of the strains induced in the initial liquefaction has a significant influence on the resistance of the sample to re-liquefaction. The deposits undergoing liquefaction experience large shear strain during liquefaction. And this previous strain changes the microstructure into highly anisotropic structure such as columnlike structure and connected voids. This type of anisotropy is so unstable that it can reduce re-liquefaction resistance. It is blown that the extent of anisotropic structural change depends on the gradation characteristics of ground. The purpose of this study is to estimate the correlation between the gradation characteristics of the sand and the ratio of re-liquefaction resistance to liquefaction resistance. In this study, 1-g shaking table tests were carried out on five different kinds of sands. During the tests the values of excess pore pressure at various depths and surface settlements were measured. Re-liquefaction resistances were not affected by the initial void ratio and the effective confining pressures, and the deposits of all test sands which had once been liquefied were reliquefied in the cyclic loading number below 1 to 1.5. The ratio of re-liquefaction resistance to liquefaction resistance linearly decreased as $D_{10}/C_u$ increased, and was constant as about 0.2 above the value of $D_{10}/C_u$, 0.15 mm.