In this paper, we propose a fast single image dehazing method based on positive correlation. Firstly, a linear model is built to describe the positive correlation between the minimum channel of the hazy image and its corresponding depth map. Then, the transmission map and the atmospheric light are separately obtained using the created linear model. Finally, based on the traditional atmospheric scattering model, the haze-free image can be recovered with the transmission map and the atmospheric light. Experimental results on numerous hazy images demonstrate that proposed method has better performance and lower time complexity than the state-of-the-art methods.