Hyperspectral images (HSIs) are crucial for many research works. Spectral super-resolution (SSR) is a method used to obtain high-spatial-resolution (HR) HSIs from HR multispectral images. Traditional SSR methods include model-driven algorithms and deep learning. By unfolding a variational method, this article proposes an optimization-driven convolutional neural network (CNN) with a deep spatial-spectral prior, resulting in physically interpretable networks. Unlike the fully data-driven CNN, auxiliary spectral response function (SRF) is utilized to guide CNNs to group the bands with spectral relevance. In addition, the channel attention module (CAM) and the reformulated spectral angle mapper loss function are applied to achieve an effective reconstruction model. Finally, experiments on two types of data sets, including natural and remote sensing images, demonstrate the spectral enhancement effect of the proposed method, and also, the classification results on the remote sensing data set verified the validity of the information enhanced by the proposed method.