In this paper, we consider the r-th inverse moment of the n-fold convolution of the zero-truncated negative binomial distribution Gr(k; n). We mainly discuss the first and second inverse moments of this distribution. We derive some recursive formulas for Gr(k; n). In particular, we give some asymptotic approximations for the first and second inverse moments of the n-fold convolution of the zero-truncated negative binomial distribution.