Superpixels technique has drawn much attention in computer vision applications. Each superpixels algorithm has its own advantages. Selecting a more appropriate superpixels algorithm for a specific application can improve the performance of the application. In the last few years, superpixels are widely used in polarimetric synthetic aperture radar image classification. However, no superpixel algorithm is especially designed for image classification. It is believed that both mixed superpixels and pure superpixels exist in an image. Nevertheless, mixed superpixels have negative effects on classification accuracy. Thus, it is necessary to generate superpixels containing as few mixed superpixels as possible for image classification. In this paper, first, a novel superpixels concept, named fuzzy-superpixels, is proposed for reducing the generation of mixed superpixels. In fuzzy-superpixels, not all pixels are assigned to a corresponding superpixel. We would rather ignore the pixels than assign them to improper superpixels. Second, a new algorithm is proposed to generate fuzzy-superpixels for PolSAR image classification. Three PolSAR images are used to verify the effect of the proposed fuzzy superpixels algorithm. Experimental results demonstrate the superiority of the proposed fuzzy-superpixels algorithm over several state-of-the-art superpixels algorithms.