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Domain adaptation (DA) aims to transfer knowledge from a label-rich but heterogeneous domain to a label-scare domain, which alleviates the labeling efforts and attracts considerable attention. Different from previous methods focusing on learning domain-invariant feature representations, some recent methods present generic semi-supervised learning (SSL) techniques and directly apply them to DA tasks, even achieving competitive performance. One of the most popular SSL techniques is pseudo-labeling that assigns pseudo labels for each unlabeled data via the classifier trained by labeled data. However, it ignores the distribution shift in DA problems and is inevitably biased to source data. To address this issue, we propose a new pseudo-labeling framework called Auxiliary Target Domain-Oriented Classifier (ATDOC). ATDOC alleviates the classifier bias by introducing an auxiliary classifier for target data only, to improve the quality of pseudo labels. Specifically, we employ the memory mechanism and develop two types of non-parametric classifiers, i.e. the nearest centroid classifier and neighborhood aggregation, without introducing any additional network parameters. Despite its simplicity in a pseudo classification objective, ATDOC with neighborhood aggregation significantly outperforms domain alignment techniques and prior SSL techniques on a large variety of DA benchmarks and even scare-labeled SSL tasks.