In recent years, biometric recognition technology has developed rapidly from single-mode identification to multimodal feature fusion. Identity recognition technology based on palm prints and veins is investigated extensively, and challenges persist in achieving real-time noncontact palm recognition. In this study, we use a binocular camera to simultaneously capture visible and near-infrared palm images, locate the region of interest based on palm key-point detection, and design a log-Gabor-convolution palm print and vein network. The network adopts a dual-branch parallel feature-extraction structure and designs a parameter-adaptive log Gabor convolution and multi-receptive-field feature-fusion module, thus significantly improving the ability to extract texture features from dual-mode images. Method testing was conducted on two publicly available palm-print and palm-vein datasets, i.e., CASIA-PV and TJU-PV, respectively, as well as on a custom-developed dataset, SWUST-PV. Experimental results show that the proposed method achieved a recognition accuracy exceeding 99.9%, with an error rate of 0.0012% or less. Compared with the basic model, the proposed model is lightweight and decreases the model parameter count and floating-point computational complexity by 76% and 81%, respectively.