Capsule network is a new type of deep learning network, capsule structure can encode information such as posture, texture, hue, etc. of the feature, and has a good ability to express the texture feature of the image. Aiming at the problem that the primary feature extraction network of the capsule network is too simple and the feature expression ability is insufficient, a discrete wavelet capsule network (DWTCapsNet) that combines the feature expression capabilities of deep convolutional neural networks with wavelet transform multi-resolution analysis capabilities is propose in this work. First, the feasibility of the capsule network in the application of texture image classification is studied. Second, the ability of each part of DWTCapsNet on the improvement of capsule network classification performance is studied. Finally, the robustness of DWTCapsNet is analyzed through anti-rotation and anti-noise experiments. The classification accuracy is used as the standard model evaluation criteria, and the experimental results on the commonly used texture image data sets show that the classification accuracy of DWTCapsNet is higher.