A Hyperspectral Image (HSI) contains a great number of spectral bands for each pixel; however, the spatial resolution of HSI is low. Hyperspectral image super-resolution is effective to enhance the spatial resolution while preserving the high-spectral-resolution by software techniques. Recently, the existing methods have been presented to fuse HSI and Multispectral Images (MSI) by assuming that the MSI of the same scene is required with the observed HSI, which limits the super-resolution reconstruction quality. In this paper, a new framework based on domain transfer learning for HSI super-resolution is proposed to enhance the spatial resolution of HSI by learning the knowledge from the general purpose optical images (natural scene images) and exploiting the cross-correlation between the observed low-resolution HSI and high-resolution MSI. First, the relationship between low- and high-resolution images is learned by a single convolutional super-resolution network and then is transferred to HSI by the idea of transfer learning. Second, the obtained Pre-high-resolution HSI (pre-HSI), the observed low-resolution HSI, and high-resolution MSI are simultaneously considered to estimate the endmember matrix and the abundance code for learning the spectral characteristic. Experimental results on ground-based and remote sensing datasets demonstrate that the proposed method achieves comparable performance and outperforms the existing HSI super-resolution methods.