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Domain adaptation (DA) aims to transfer knowledge from a label-rich and related domain (source domain) to a label-scare domain (target domain). Pseudo-labeling has recently been widely explored and used in DA. However, this line of research is still confined to the inaccuracy of pseudo-labels. In this paper, we reveal an interesting observation that the target samples belonging to the classes with larger domain shift are easier to be misclassified compared with the other classes. These classes are called hard class, which deteriorates the performance of DA and restricts the applications of DA. We propose a novel framework, called Hard Class Rectification Pseudo-labeling (HCRPL), to alleviate the hard class problem from two aspects. First, as is difficult to identify the target samples as hard class, we propose a simple yet effective scheme, named Adaptive Prediction Calibration (APC), to calibrate the predictions of the target samples according to the difficulty degree for each class. Second, we further consider that the predictions of target samples belonging to the hard class are vulnerable to perturbations. To prevent these samples to be misclassified easily, we introduce Temporal-Ensembling (TE) and Self-Ensembling (SE) to obtain consistent predictions. The proposed method is evaluated in both unsupervised domain adaptation (UDA) and semi-supervised domain adaptation (SSDA). The experimental results on several real-world cross-domain benchmarks, including ImageCLEF, Office-31 and Office-Home, substantiates the superiority of the proposed method.