To address the issue that the difficult parameter selection or poor interpretability caused by the existing hyperspectral super-resolution methods rely on manual or data-driven prior, a deep prior regularization-based hyperspectral image super-resolution method was adopted for theoretical analysis and experimental validation. First, a multi-stage feature extraction network based on a deep convolutional neural network was designed to extract spatial and spectral information from the degraded images. Then, the collected spatial-spectral prior features were fed into a transformer-based feature fusion module, where complementary information from the spatial and spectral domains was adaptively extracted to capture the image’s global prior features. Finally, the super-resolution problem of the image was formulated as an optimization problem by inserting deep prior regularization term in the degraded model, the solution of which can be achieved using the alternating direction method of multipliers while minimizing solution complexity. Experimental results show that reconstruction signal-to-noise ratio of this algorithm is 34.16 dB and 29.35 dB when both of the signal-to-noise ratio are 35 dB, which is 2.78 dB and 2.17 dB higher than the suboptimal algorithm, respectively. The reconstructed high-resolution hyperspectral images have high consistency with their inherent structures under the condition of deep prior regularization. This study provides a reference for the combined use of manual and data-driven prior to enhance the spatial resolution of hyperspectral images.