Over the past two decades, several studies have paid great attention to biometric palmprint recognition. Recently, most methods in literature adopted deep learning due to their high recognition accuracy and the capability to adapt with different acquisition palmprint images. However, high-dimensional data with a large number of uncorrelated and redundant features remain a challenge due to computational complexity issues. Feature selection is a process of selecting a subset of relevant features, which aims to decrease the dimensionality, reduce the running time, and improve the accuracy. In this paper, we propose efficient unimodal and multimodal biometric systems based on deep learning and feature selection. Our approach called simplified PalmNet–Gabor concentrates on the improvement of the PalmNet for fast recognition of multispectral and contactless palmprint images. Therefore, we used Log-Gabor filters in the preprocessing to increase the contrast of palmprint features. Then, we reduced the number of features using feature selection and dimensionality reduction procedures. For the multimodal system, we fused modalities at the matching score level to improve system performance. The proposed method effectively improves the accuracy of the PalmNet and reduces the number of features as well the computational time. We validated the proposed method on four public palmprint databases, two multispectral databases, CASIA and PolyU, and two contactless databases, Tongji and PolyU 2D/3D. Experiments show that our approach achieves a high recognition rate while using a substantially lower number of features.