In Domain Adaptation (DA), the category-relevant losses usually occupy a dominant position, while they are usually built with hard or soft labels in existing models. We observed that hard labels are overconfident due to hard samples existed, and soft labels are ambiguous as too many small noisy probabilities involved, and both of them are easily to cause negative transfer. Besides, the category-irrelevant losses in Closed-Set DA (CSDA) paradigm fail to work in Open-Set DA (OSDA), and they also have to be in a category-relevant form, since target data samples are split into shared and private classes. To this end, we propose a newly-unified DA framework (i.e., Importance Filtered Cross-Domain Adaptation, IFCDA). Firstly, an importance filtered mechanism is devised to generate filtered soft labels to mitigate negative transfer desirably. Specifically, the soft labels are divided into confident and ambiguous ones. Then, only the maximum probability in each confident label is retained, and a threshold value is set to truncate each ambiguous label so that only prominent probabilities are reserved. Moreover, a general graph-based label propagation is contrived to attain soft labels in both CSDA and OSDA, where an extra component is embedded into label vector, so that it could detect target novel classes. Finally, the category-relevant losses in both scenarios are reformulated using filtered soft labels, while the category-irrelevant MMD loss in CSDA is reformulated as a form like class-wise MMD using newly-designed importance filtered soft labels. Notably, CSDA paradigm is a special case when all extra components are set to 0, thus the proposed approach is geared to both CSDA and OSDA. Comprehensive experiments on benchmark cross-domain object recognition datasets verify that the proposed approach outperforms several state-of-the-art methods in both scenarios.