All computation of surface area of images in various scales is performed in the original image by conventional computing method of fractal dimension. The algorithms are inconsistent with the fact that the details of image could change when the metric scale varies, as a result, the span of the fractal dimension in the same kind of ground object is too big and goes against the image segmentation and image classification. To solve this problem, a fast interpolation algorithm based on area weight is put forward to simulate the images with various scales, which is used to calculate the fractal dimension of image. Experimental results show that the proposed method speeds up to 10 times faster and has less variance within clusters than the conventional method according to the standard Lena image. In addition, it can resist image noise well. Therefore, the proposed algorithm is applicable to image segmentation or image classfication.