Abstract: This paper aims at developing a covariate selection approach for high-dimensional covariate vector in the presence of nonignorable nonresponse. Because of nonignorable missing responses, a novel covariate selection method has to be developed to eliminate covariates associated with neither the response variable nor the nonresponse mechanism. Once the redundant covariates are removed, existing methods for propensity estimation and other analyses by inverse propensity weighting can be applied. We provide some simulation results to show the effectiveness of our approach.