Limited by the existing imagery sensors, hyperspectral images are characterized by high spectral resolution but low spatial resolution. The super-resolution (SR) technique aiming at enhancing the spatial resolution of the input image is a hot topic in computer vision. In this paper, we present a hyperspectral image (HSI) SR method based on a deep information distillation network (IDN) and an intra-fusion operation. Specifically, bands are firstly selected by a certain distance and super-resolved by an IDN. The IDN employs distillation blocks to gradually extract abundant and efficient features for reconstructing the selected bands. Second, the unselected bands are obtained via spectral correlation, yielding a coarse high-resolution (HR) HSI. Finally, the spectral-interpolated coarse HR HSI is intra-fused with the input HSI to achieve a finer HR HSI, making further use of the spatial-spectral information these unselected bands convey. Different from most existing fusion-based HSI SR methods, the proposed intra-fusion operation does not require any auxiliary co-registered image as the input, which makes this method more practical. Moreover, contrary to most single-based HSI SR methods whose performance decreases significantly as the image quality gets worse, the proposal deeply utilizes the spatial-spectral information and the mapping knowledge provided by the IDN, which achieves more robust performance. Experimental data and comparative analysis have demonstrated the effectiveness of this method.