Banach space geometry theory is an important direction of modern functional analysis theory. As aspecific category of Banach spaces，Orlicz space contains many classic Banach spaces. In order to intensive studythe Orlicz space theory，through the study of geometric constants in Orlicz sequence spaces with p-Amemiya norm，the concrete value of Garcia-Falset coefficient R( X) is obtained with conditions. The geometric constants of the Orlicz sequence space with the p-Amemiya norm are filled in the blank in computing. The geometric theory of Orliczspaces with the p-Amemiya norm is enriched