In order to recognize breast cancer histopathological images, this article proposed a combined model consisting of a pyramid gray level co-occurrence matrix (PGLCM) feature extraction model and an incremental broad learning (IBL) classification model. The PGLCM model is designed to extract the fusion features of breast cancer histopathological images, which can reflect the multiresolution useful information of the images and facilitate the improvement of the classification effect in the later stage. The IBL model is used to improve the classification accuracy by increasing the number of network enhancement nodes horizontally. Unlike deep neural networks, the IBL model compresses the training and testing time cost greatly by making full use of its single-hidden-layer structure. To our knowledge, it is the first attempt for the IBL model to be introduced into the breast cancer histopathological image recognition task. The experimental results in four magnifications of the BreaKHis dataset show that the accuracy of binary classification and eight-class classification outperforms the existing algorithms. The accuracy of binary classification reaches 91.45%, 90.17%, 90.90% and 90.73%, indicating the effectiveness of the established combined model and demonstrating the advantages in breast cancer histopathological image recognition.