This paper proposes a powerful SVM-ASM filter, the adaptive switching median(ASM) filter based on support vector machines(SVMs), to effectively reduce impulse noise in corrupted images while preserving image details and features. The proposed SVM-ASM filter is composed of two stages: SVM impulse detection and ASM filtering. SVM impulse detection determines whether the pixels are corrupted by noise or not according to an optimal discrimination function. ASM filtering implements the image filtering with a variable window size to effectively remove the noisy pixels determined by the SVM impulse detection. Experimental results show that the SVM-ASM filter performs significantly better than many other existing filters for denoising impulse noise even in highly corrupted images with regard to noise suppression and detail preservation. The SVM-ASM filter is also extremely robust with respect to various test images and various percentages of image noise.