Classification of textures based on wavelet pattern analysis is one of the most effective methods in texture classification. However using all frequency sub-bands in decomposition for classification may increase time complexity of classification algorithms. To reduce the time complexity, sub-bands with high energy and entropy are selected for classification. Fractal dimension can be used to select such significant sub-bands for decomposition at each level. Further statistical features of these significant sub-bands are given to modified K-NN classifier for classification. This paper describes texture classification using sub-bands of wavelets based on fractal dimensions and their results are compared with the results of texture classification using conventional features and also with different classifiers. Success rate is very high and time complexity is also reduced to the order of O(n).