Existing dehazing methods face challenges in generalization due to the lack of paired real-world training data and tailored models. Recently, some semi-supervised/unsupervised schemes have been explored, achieving impressive performance. However, their performance still depends heavily on synthetic training data and the introduced prior-based strong constraints do not always hold. In this paper, we first introduce RealHQ-HAZE, a new dataset with 200 collected real-world hazy images, 200 corresponding carefully rendered haze-free images, and an additional 1000 varicolored hazy images transferred from the collected images. We also propose a prior-compensated multi-stage dehazing network, PMDN, which can learn different levels of real-world haze distribution through multi-stage progressive learning. To utilize prior knowledge effectively, we introduce a prior-based feature compensation module, guiding intermediate results with an adaptive weight. Additionally, we propose a MixCut consistent dehazing strategy to mix paired and derived images using a cross-cutting scheme, reinforcing dehazing through consistency principles. Extensive experiments demonstrate the effectiveness of our dataset and the superiority of PMDN compared to existing state-of-the-art dehazing methods.