Recently deep convolutional neural network (CNN) has made significant achievement in Single Image Super-Resolution (SISR). Most CNN-based SISR methods used the default L2 norm of the error. However, for Hyperspectral Image (HSI), this loss function may bring spectral inconsistencies. The main reason is that most methods did not pay much attention to spectral loss. To HSI, the loss function should capture not only spatial information but also spectral consistency. In this paper, a Multi-Losses Function Network (MLFN) simultaneously considering spatial and spectral information is proposed, and is composed of two parts: one is Concatenate Dense Residual Network (CDRN), and the other is Loss Network (LN). CDRN is an image reconstruction network which can utilize the hierarchical features extracted from the low-resolution image. LN includes pixel-wise spatial loss and spectral loss which drive the learning of the entire reconstruction model. The experimental results prove that the proposed MLFN can enhance spatial resolution with the consistency of the spectrum of HSI preserved.