Compressive coded hyper spectral (HS) imaging actualizes compressed sampling and snapshot acquisition of HS data, whereas current recovery algorithms take too long time to make real-time HS imaging satisfactory. This paper proposes a deep learning approach for compressive HS imaging to shorten the recovery time. A fully-connected network is designed to train a block-based non-linear reconstruction operator. There is a mergence after obtaining the recovery 3D blocks, followed with a block edge mean filter. The contribution of this approach is that it uses deep neural network to do the reconstruction of the HS data for the first time and it has low-complexity and needs less memory because of operating on local patches. The proposed method was validated on a public available HS dataset and the experimental results show that this approach is superior to the state-of-the-art in the recovery accuracy, and dramatically improves the reconstruction speed by 400 similar to 760 times.