For the sensitivity analysis of failure probability with dependent input variables, by introducing the copula function to describe the joint probability distribution of input variables, the reliability sensitivity can be decomposed into independent sensitivity and dependent sensitivity, which can be used to measure the influence of distribution param-eters separately. Since the parameters of multivariate copula function are difficult to be determined, the bivariate copulas are preferred in practice. Then the D-vine copula model is employed to transform the multivariate joint probability density function (PDF) into the product of multiple bivariate copulas and marginal PDF of all variables. Based on the copula theory, the computation of sensitivity with dependent variables can be transformed into the computation of kernel function of marginal PDF and copula kernel function of a group of bivariate copulas, which can be derived analytically. The general numerical approach is used to compute the separate sensitivity. Then, test examples are employed to validate the rationality of the proposed method.