The combination of single-pixel imaging and single photon-counting technology enables ultra-high-sensitivity photon-counting imaging. In order to shorten the reconstruction time of single-photon counting, the algorithm of compressed sensing is used to reconstruct the underdetermined image. Compressed sensing theory based on prior constraints provides a solution that can achieve stable and high-quality reconstruction, while the prior information generated by the network may overfit the feature extraction and increase the burden of the system. In this paper, we propose a novel sparse autoencoder network prior for the reconstruction of the single-pixel imaging, and we also propose the idea of multi-channel prior, using the fully connected layer to construct the sparse autoencoder network. Then, take the network training results as prior information and use the numerical gradient descent method to solve underdetermined linear equations. The experimental results indicate that this sparse autoencoder network prior for the single-photon counting compressed images reconstruction has the ability to outperform the traditional one-norm prior, effectively improving the reconstruction quality.