In this paper, an attempt has been made in proposing some improved estimators of finite population variance when random non-response is present in the study variable, on the estimators given by Sharma and Singh (2018). Four improved regression type estimators have been proposed using information on two auxiliary variables, one of which has missing values in the data, using two-phase sampling scheme. Different robust regression methods have been applied on the proposed techniques so as to improve the efficiency of the estimators in case of outliers. It has been observed that robust estimators are more efficient than the proposed ones under some conditions. All the proposed estimators are compared with existing estimators for different values of probability of non-response and the results are verified by using empirical and simulation studies.