There are several statistical descriptors for feature extraction from texture images. Local binary pattern is one of the most popular descriptor for revealing the underlying structure of a texture. Recently several variants of local binary descriptor have been proposed. The completed local binary pattern is an efficient version that can provide discriminant features and consequently providing a high classification rate. It finely characterizes a texture by fusing three histograms of features. Fusing histograms is applied by jointing the histograms and it increases the feature number significantly; therefore, in this paper a weighted constraint feature selection approach is proposed to select a very small number of features without any degradation in classification accuracy. It significantly enhances the classification rate by using a very low number of informative features. The proposed feature selection approach is a filter-based feature selection. It employed a weighted constraint score for each feature. After ranking the features, a threshold estimation method is proposed to select the most discriminant features. For a better comparison, a wide range of different datasets is used as benchmark to assess the compared methods. Implementations on Outex, UIUC, CUReT, MeasTex, Brodatz, Virus, Coral Reef, and ORL face datasets indicate that the proposed method can provide high classification accuracy without any learning step just by selecting a few features of descriptor.