Fractal Dimension is a basic parameter of fractal geometry and it has been applied in many fields of application including image analysis, texture segmentation, and shape classification. Many fractal dimensions methods have been evolved depending upon different types of images that could be differentiated with greater precision. In this paper, we propose a color approach based on the modified differential box-counting method to estimate fractal dimension of color images in terms of its smoothness. Here we have experimented on four sets of color images like; sixteen number of real natural texture images, eight sets of controlled experimental fabric images with varied color and texture, twelve numbers of generated synthetic images and four smoothed images of known fractal dimension. The results demonstrated that the said proposed method shows accurate fractal dimension estimation of color texture image and also it indicates FD as 2 for smoothed images, which has already been developed in last decade and indicates higher roughness in color images, to check the accuracy of our proposed method, we used a set of twelve synthetic generated images.