Despite natural image super-resolution (SR) methods have achieved great success, super-resolution methods for hyperspectral image (HSI) with rich spectral features are still a very challenging task. Furthermore, due to the diversity of HSI captured by different cameras, their degradation conditions vary. Currently available HSI SR methods are mainly based on fixed degradation models, and their performance is severely affected when the actual degradation does not match the assumed degradation model. To address this issue, this paper proposes a single-band hyperspectral image super-resolution (SBHSR) method for HSI. This method assumes that the degradation Gaussian blur kernel parameters of the HSI are unknown, and adapts to various degradation conditions by conducting blind super-resolution on the image. It also combines another band with better spatial structure as an auxiliary band for feature fusion. To address the spectral differences between the super-resolution band and the auxiliary band, we use the Spatial Adaptation Module (SAM) to map the feature distribution, ensuring consistent spectral brightness between the auxiliary band and the super-resolution band. Due to the use of blind degradation super-resolution method, our method is more robust compared to previous HSI SR methods. Additionally, as it is specifically designed for single-band hyperspectral image super-resolution, it has the advantage of being faster and more efficient. Experimental validation on two hyperspectral datasets demonstrates the superiority of our method, as it improves the spatial resolution of the image while preserving the spectral features, and performs better than existing blind super-resolution methods.