Deep learning-based hyperspectral image (HSI) classification methods have recently shown excellent performance, however, there are two shortcomings that need to be addressed. One is that deep network training requires a large number of labeled images, and the other is that deep network needs to learn a large number of parameters. They are also general problems of deep networks, especially in applications that require professional techniques to acquire and label images, such as HSI and medical images. In this paper, we propose a deep network architecture (SAFDNet) based on the stochastic adaptive Fourier decomposition (SAFD) theory. SAFD has powerful unsupervised feature extraction capabilities, so the entire deep network only requires a small number of annotated images to train the classifier. In addition, we use fewer convolution kernels in the entire deep network, which greatly reduces the number of deep network parameters. SAFD is a newly developed signal processing tool with solid mathematical foundation, which is used to construct the unsupervised deep feature extraction mechanism of SAFDNet. Experimental results on three popular HSI classification datasets show that our proposed SAFDNet outperforms other compared state-of-the-art deep learning methods in HSI classification.