In this paper, we propose a novel semi-supervised speaker identification method that can alleviate the influence of nonstationarity such as session dependent variation, the recording environment change, and physical condition/emotion. We assume that the utterance variation follows the covariate shift model, where only the utterance sample distribution changes in the training and test phases. Our method consists of weighted versions of kernel logistic regression and crossvalidation and is theoretically shown to have the capability of alleviating the influence of covariate shift. We experimentally show through text-independent speaker identification simulations that the proposed method is promising in dealing with variations in session dependent utterance variation.