It is important to apply models trained on a large number of labeled samples to different domains because collecting many labeled samples in various domains is expensive. To learn discriminative representations for the target domain, we assume that artificially labeling the target samples can result in a good representation. Tri-training leverages three classifiers equally to provide pseudo-labels to unlabeled samples; however, the method does not assume labeling samples generated from a different domain. In this paper, we propose the use of an \textit{asymmetric} tri-training method for unsupervised domain adaptation, where we assign pseudo-labels to unlabeled samples and train the neural networks as if they are true labels. In our work, we use three networks \textit{asymmetrically}, and by \textit{asymmetric}, we mean that two networks are used to label unlabeled target samples, and one network is trained by the pseudo-labeled samples to obtain target-discriminative representations. Our proposed method was shown to achieve a state-of-the-art performance on the benchmark digit recognition datasets for domain adaptation.