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To overcome the staircase effects and simultaneously avoid edge blurring, here the authors proposed a novel algorithm of adaptive fourth-order partial differential equation (PDE) for image smoothing. The proposed method is based on You and Kaveh (YK) model that first performs a pre-processing using coherence-enhancing diffusion filter before the smoothing. Then, the authors select an adaptive edge-stopping function founded on the Tansig function to effectively remove the noise and insignificant details without destruction of important edges and textures in the image. MATLAB simulation results validate the efficiency of the proposed model quantitatively and visually, when compared with other state-of-the-art methods.