Computed tomography imaging spectrometry (CTIS) is a snapshot hyperspectral imaging (HSI) technique capable of capturing projections of the target scene from multiple wavelengths in one single exposure. The CTIS inversion problem is usually very challenging, and solving it from a single snapshot measurement often requires time-consuming iterative algorithms. And most deep learning-based algorithms in computational imaging need the priori of many samples, which brings a heavy data collection burden. In this article, to reconstruct hyperspectral cubes from CTIS measurements in an efficient way, we introduce a new CITS framework named ASP-Model based on the angular spectrum propagation theory to model the forward CITS process and efficiently reconstruct hyperspectral. Specifically, our method acquires simulation data using angular spectrum propagation for training and reconstructs real data captured by our custom-built CTIS system during inference. This framework allows us to eliminate the need to acquire extensive real data for network training. Moreover, the proposed network can reconstruct 26 spectral channels from one single measurement and demonstrates state-of-the-art results over existing reconstruction algorithms both in simulation and experimental results. We also release a new dataset containing simulated and real CTIS data for public comparison. The code and dataset are publicly available at https://github.com/YifanSi/ASP_Model.