In order to address the problems of discontinuity and block effect for the dehazing method based on dark channel prior, we improved this method using wavelet decomposition, fast kernel regression model, and bicubic interpolation. First, spatial resolution of the hazy image was reduced by the downsampling method with Haar wavelet decomposition. Second, the fast kernel regression model was proposed to smooth the central transmission with local neighbor transmissions. Last, the smoothed transmission for the approximation image was resized to the hazy image by the bicubic interpolation method. Experiments were carried out on synthetic hazy images with known ground truth and real-world hazy images without ground truth. The regions of sudden change of depth in the dehazed images by our method were more smooth and continuous than those of several state-of-the-art methods, and contrast of our method was higher than that of other methods. Indexes based on the concept of visibility level, mean squared error, and structural similarity of our method were better than those of other methods.