Recently, the classification of surface textures is carried out using various modelling approaches. To analyse the surface texture, most of the techniques uses large amount of training data which adds up to considerable computational cost. However, the implementation of various neural network models also requires significant amount of training images to classify surface textures. In the proposed paper, a deep learning-based model is presented using convolution neural network (CNN). Further, this model is divided into two sub models knowing model-1 and model-2. The approach is designed with customized parameters configuration to classify surface texture using a smaller number of training samples. The image feature vectors are generated using statistical operations to compute the physical appearance of the surface and a CNN model is used to classify the generated surfaces with appropriate labels into classes. The Kylberg Texture dataset is used to evaluate the proposed models using 16 texture classes. The advantage of proposed models over pre-trained networks is that the entire models is customized according to specific training requirements. Further, to demonstrate the state-of-the-art results, the proposed approach is compared with other existing techniques. Our experimental results are better than the conventional techniques and achieves an accuracy of 92.42% for model-1 and 96.36% for model-2. In addition, the proposed models maintain balance between accuracy and computational cost.