Texture classification is an active area of research in the field of pattern recognition. Convolutional neural networks (CNNs) have a remarkable capability of recognizing patterns and are one of the most efficient deep learning techniques. But, finding the optimal values of the different hyperparameters of the CNN is a major challenge. Nature-inspired algorithms (NIAs) are the meta-heuristic algorithms well-known for their optimizing capability. Whale optimization algorithm (WOA) is a recent nature-inspired algorithm (NIA) that is inspired by the hunting behaviour of the humpback whales. In this paper, we propose a novel deep learning technique for texture recognition using a CNN optimized through WOA. We apply WOA at the two different levels in the CNN: In the convolutional layer (for optimizing the values of the filters), and in the fully-connected layer (for optimizing the values of the weights and biases). For examining the performance of our technique, we apply it to the following three benchmark texture datasets: Kylberg v1.0, Brodatz, and Outex_TC_00012. Our model performs better than the most of the existing methods for the Kylberg and the Outex_TC_00012 datasets and gives competitive results for the Brodatz dataset. It is evident from the results that our model has the potential for application in the field of texture recognition.