Based on the tensor truncated nuclear norm and the spatial-spectral total variation regularization,a new model is proposed to realize super-resolution reconstruction of hyperspectral images to solve the problem that most hyperspectral images suffer from degradation in the acquisition process. First, two types of priori information in the hyperspectral images, i. e., the low rank-based priori information and sparse priori in the spatial and spectral domain, are explored. Next, using the low rank-based priori information in the spatial and spectral domain, a low-rank constraint model based on the tensor truncated nuclear norm is proposed to achieve a more accurate approximation of the rank function. Subsequently, using sparse priori information in the spatial and spatial domain, a spatial and spectral total variation regularization model is proposed to retain the sharp edges and more detailed information of the original image. Finally, the low-rank constraint model based on the tensor truncated nuclear norm and spatial and spectral total variation models are integrated. This new restoration model possesses the advantages of both the aforementioned models. The peak signal-to-noise ratio of 0.8 dB is obtained, and structural similarity indices are adopted to provide quantitative assessments of experimental results. The experimental results demonstrate that the proposed model achieves better visual quality than those of several existing related methods. The proposed model can effectively achieve the super-resolution reconstruction of hyperspectral images after being blurred and downsampled.