In this paper, we propose a novel semi-supervised speaker identification method that can alleviate the influence of non-stationarity such as session dependent variation, the recording environment change, and physical conditions/emotions. We assume that the voice quality variants follow the covariate shift model, where only the voice feature distribution changes in the training and test phases. Our method consists of weighted versions of kernel logistic regression and cross validation and is theoretically shown to have the capability of alleviating the influence of covariate shift. We experimentally show through text-independent/dependent speaker identification simulations that the proposed method is promising in dealing with variations in voice quality. Keywords Speaker identification, covariate shift, semi-supervised learning, kernel logistic regression, importance estimation.