In this paper, we will investigate the approximations of inverse moments for double-indexed weighted sums of random variables under sub-linear expectations. The asymptotic approximations of inverse moments and the convergence rate of approximations are established under the meaning of upper expectation and the lower expectation, respectively. The results obtained in the paper improve and extend the corresponding ones of Yang et al. (2016) from independent random variables in the classical probability space to END random variables in sub-linear expectation space.