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Compared with multi-class classification, multi-label classification that contains more than one class is more suitable in real life scenarios. Obtaining fully labeled high-quality datasets for multi-label classification problems, however, is extremely expensive, and sometimes even infeasible, with respect to annotation efforts, especially when the label spaces are too large. This motivates the research on partial-label classification, where only a limited number of labels are annotated and the others are missing. To address this problem, we first propose a pseudo-label based approach to reduce the cost of annotation without bringing additional complexity to the existing classification networks. Then we quantitatively study the impact of missing labels on the performance of classifier. Furthermore, by designing a novel loss function, we are able to relax the requirement that each instance must contain at least one positive label, which is commonly used in most existing approaches. Through comprehensive experiments on three large-scale multi-label image datasets, i.e. MS-COCO, NUS-WIDE, and Pascal VOC12, we show that our method can handle the imbalance between positive labels and negative labels, while still outperforming existing missing-label learning approaches in most cases, and in some cases even approaches with fully labeled datasets.