Abstract: Using image classification method based on deep learning are outstanding for pathological diagnosis. However, the noise generated in the process of obtaining pathological slices can affect the generalization performance of the network, thereby reducing the accuracy of the classification algorithm. In response to this problem, the paper proposes a new robust pathological image classification method — multi-scale wavelet pooling covariance (MWPC) network. MWPC network is composed of four core modules: wavelet pooling layer, composite convolution layer, multi-scale feature fusion layer and covariance feature extraction layer. Wavelet pooling layer can suppress the influence of noise while protecting effective features from loss.The accuracy rate can reach 90.90% under noise-free conditions, which is 1.68% higher than ResNet and 0.43% higher than Inception-v3. Under the conditions of simulated salt and pepper noise, Gaussian noise and Cauchy noise, the noise robustness of MWPC is significantly improved, which also reduces the mean noise error. The ablation experiment about network modules shows that the MWPC network can improve performance and noise robustness. Multi-scale feature fusion layer combines the shallow features with the image features, so that the image features can retain more image details. Covariance feature extraction layer can obtain high-order statistical features of the image, and improve the generalization performance of the network. On the clinical data set, the proposed MWPC network in the paper is aimed at the five-class task of histopathological image patches.The accuracy rate can reach 90.90% under noise-free conditions, which is 1.68% higher than ResNet and 0.43% higher than Inception-v3. Under the conditions of simulated salt and pepper noise, Gaussian noise and Cauchy noise, the noise robustness of MWPC is significantly improved, which also reduces the mean noise error. The ablation experiment about network modules shows that the MWPC network can improve performance and noise robustness.