Most learning-based methods previously used in image dehazing employ a supervised learning strategy, which is time-consuming and requires a large-scale dataset. However, large-scale datasets are difficult to obtain. Here, we propose a self-supervised zero-shot dehazing network (SZDNet) based on dark channel prior, which uses a hazy image generated from the output dehazed image as a pseudo-label to supervise the optimization process of the network. Additionally, we use a novel multichannel quad-tree algorithm to estimate atmospheric light values, which is more accurate than previous methods. Furthermore, the sum of the cosine distance and the mean squared error between the pseudo-label and the input image is applied as a loss function to enhance the quality of the dehazed image. The most significant advantage of the SZDNet is that it does not require a large dataset for training before performing the dehazing task. Extensive testing shows promising performances of the proposed method in both qualitative and quantitative evaluations when compared with state-of-the-art methods.