The advent of small-world network theory has significantly revolutionized network science. Small-world networks, characterized by high clustering coefficients and short average path lengths, amalgamate the beneficial aspects of both regular and random graphs. These networks exhibit unique properties such as regional specialization and enhanced efficiency in information transmission. Leveraging this phenomenon, we propose a novel approach to augment the training efficiency of deep convolutional neural networks (CNNs). This work introduces a novel architecture, the Small World Convolutional Neural Network (swCNN), inspired by small-world network dynamics. swCNN leverages a small-world inspired design to speed up feature extraction, enhancing training efficiency with faster convergence and improved learning dynamics. The efficacy of swCNN is rigorously evaluated using a suite of benchmark datasets, including MNIST, QMNIST, Fashion MNIST, CIFAR10, STL 10, USPS and APTOS. The experiments show that swCNN makes training more efficient, leading to faster and better development of CNN architectures based on small-world network concepts.