In this study, we propose the robust ratio-type estimator of finite population variance considering the minimum covariance determinant (MCD) and the minimum volume ellipsoid (MVE) robust covariance matrices in simple and stratified random sampling. The mean square errors (MSE) equations are obtained for the robust ratio-type estimator. The conditions for which the proposed robust ratio-type estimator is more efficient as compared to competing estimators have been discussed. The MCD and MVE are robust against outliers. Thus, when there is an outlier in the data, simulations and empirical results show that the proposed robust ratio-type estimators under simple and stratified random sampling have a lower mean square error than the traditional estimators. In addition, we support theoretical results with contaminated real examples and simulation studies.