Removing non-homogeneous haze from real-world images is a challenging task. Meanwhile, the popularity of high-definition imaging systems and compute-limited smart mobile devices has resulted in new problems, such as the high computational load caused by haze removal for large-size images, or the severe information loss caused by the degradation of both the haze and image downsampling, when applying existing dehazing methods. To address these issues, we propose an isomorphic dual-branch dehazing and super resolution network for non-homogeneous dehazing of a downsampled hazy image, which produces dehazed and enlarged images with sharp edges and high color fidelity. We quantitatively and qualitatively compare our network with several state-of-the-art dehazing methods under the condition of different downsampling scales. Extensive experimental results demonstrate that our method achieves superior performance in terms of both the quality of output images and the computational load. The code is publicly available at https://github.com/lizhangray/IDBDehaze.