Multi-label classification (MLC) suffers from the inevitable label noise in training data due to the difficulty in annotating various semantic labels in each image. To mitigate the influence of noisy labels, existing methods mainly devote to identifying and correcting the label mistakes via a trained MLC model. However, these methods still involve annoying noisy labels in training, which can result in imprecise recognition of noisy labels and weaken the performance. In this paper, considering that the negative labels are substantially more than positive labels, and most noisy labels are from the negative labels, we directly discard all the negative labels in the dataset, and propose a new method dubbed positive and unlabeled multi-label classification (PU-MLC). By extending positive-unlabeled learning into MLC task, our method trains model with only positive labels and unlabeled data, and introduces adaptive re-balance factor and adaptive temperature coefficient in the loss function to alleviate the catastrophic imbalance in label distribution and over-smoothing of probabilities in training. Our PU-MLC is simple and effective, and it is applicable to both MLC and MLC with partial labels (MLC-PL) tasks. Extensive experiments on MS-COCO and PASCAL VOC datasets demonstrate that our PU-MLC achieves significantly improvements on both MLC and MLC-PL settings with even fewer annotations. Code will be released.