Hyperspectral remote sensing image (HSI) classification is very useful in different applications, and recently, deep learning has been applied for HSI classification successfully. However, the number of training samples is usually limited, causing difficulty in use of very deep learning models. We propose a wide and deep Fourier network to learn features efficiently by using pruned features extracted in the frequency domain. It is composed of multiple wide Fourier layers to extract hierarchical features layer-by-layer efficiently. Each wide Fourier layer includes a large number of Fourier transforms to extract features in the frequency domain from a local spatial area using sliding windows with given strides.These extracted features are pruned to retain important features and reduce computations. The weights in the final fully connected layers are computed using least squares. The transform amplitudes are used for nonlinear processing with pruned features. The proposed method was evaluated with HSI datasets including Pavia University, KSC, and Salinas datasets. The overall accuracies (OAs) of the proposed method can reach 99.77%, 99.97%, and 99.95%, respectively. The average accuracies (AAs) can achieve 99.55%, 99.95%, and 99.95%, respectively. The Kappa coefficients are as high as 99.69%, 99.96%, and 99.94%, respectively. The experimental results show that the proposed method achieved excellent performance among other compared methods. The proposed method can be used for applications including classification, and image segmentation tasks, and has the ability to be implemented with lightweight embedded computing platforms. The future work is to improve the method to make it available for use in applications including object detection, time serial data prediction, and fast implementation.