Hyperspectral imaging is applied in a wide range of defense, security and law enforcement applications. The spectral data caries valuable information for tasks such as identification, detection, and classification. However, the capturing of the spectral information, together with the spatial information, requires a significant acquisition effort. In the recent years we have developed several compressive hyperspectral imaging techniques demonstrating reduction of the captured data by at least an order of magnitude. However, compressive sensing techniques typically require computational heavy and time consuming iterative reconstruction algorithms. The computational burden is even more prominent in compressive spectral imaging due to the large amount of data involved. In this work we demonstrate the utilization of a convolutional neural network (CNN) for the reconstruction of spectral images captured with our Compressive Sensing-Miniature Ultraspectral Imager (CS-MUSI). We discuss the challenges of training the CNN for CS-MUSI and analyze the CNNbased reconstruction performance.