Black-Box unsupervised domain adaptation (BBUDA) learns knowledge only with the prediction of target data from the source model without access to the source data and source model, which attempts to alleviate concerns about the privacy and security of data. However, incorrect pseudo-labels are prevalent in the prediction generated by the source model due to the cross-domain discrepancy, which may substantially degrade the performance of the target model. To address this problem, we propose a novel approach that incrementally selects high-confidence pseudo-labels to improve the generalization ability of the target model. Specifically, we first generate pseudo-labels using a source model and train a crude target model by a vanilla BBUDA method. Second, we iteratively select high-confidence data from the low-confidence data pool by thresholding the softmax probabilities, prototype labels, and intra-class similarity. Then, we iteratively train a stronger target network based on the crude target model to correct the wrongly labeled samples to improve the accuracy of the pseudo-label. Experimental results demonstrate that the proposed method achieves state-of-the-art black-box unsupervised domain adaptation performance on three benchmark datasets.