Passport background texture classification has always been an important task in border checks. Current manual methods struggle to achieve satisfactory results in terms of consistency and stability for weakly textured background images. For this reason, this study designs and develops a CNN and Transformer complementary network (PBNet) for passport background texture image classification. We first design two encoders by Transformer and CNN to produce complementary features in the Transformer and CNN domains, respectively. Then, we cross-wisely concatenate these complementary features to propose a feature enhancement module (FEM) for effectively blending them. In addition, we introduce focal loss to relieve the overfitting problem caused by data imbalance. Experimental results show that our PBNet significantly surpasses the state-of-the-art image segmentation models based on CNNs, Transformers, and even Transformer and CNN combined models designed for passport background texture image classification.