The traditional median filter can handle the image salt and pepper noise better. However, when the noise intensity is large, it is often necessary to enlarge the filter window to ensure the denoising effect, but the enlarged window may also cause excessive smoothing of the image, loss of texture details, and blurred edges. In view of the strong edge preservation characteristics of variational model denoising, we propose a salt and pepper noise removal method based on the edge-adaptive total variational model. Firstly, the image is segmented into edge regions and non-edge regions by edge detection operators. Secondly, the salt and pepper noise of the image is processed using the median filter and adaptive total variation model, respectively. Lastly, the non-edge regions processed by the median filter and the edge regions processed by the adaptive total variation model are extracted for splicing. The experimental results show that the method cannot only effectively remove salt and pepper noise, but also effectively protect the main edge details of the image.