In the paper, the limit state equation of tensile reliability of foundation base of gravity dam is established. The possible crack length is set as action effect and the allowance crack length is set as resistance in this limit state. The nonlinear FEM is applied to obtain the crack length of foundation base of gravity dam, and linear response surface method based on the orthogonal test design method is used to calculate the reliability,which offered an reasonable and simple analysis method to calculate the reliability on serviceability limit state .The LongTan RCC gravity dam is taken as an example.The orthogonal test, which includes 9 factors and 2 levels, is adopted . The tensile reliability is calculated and design point are also given. The analyses results showed that this method is reasonable.