First-principles studies are cartied out on the electronic structure aed Compton profile for the low-synmmetry system of calcium dihydride using the discrete variational local-density-funational method with embedded cluster model. The results demonstrate that, with the ionic bonding picture, experimental data from photoelectron spectroscopy with both x-rays and synchrotron radiation and from Compton profile measurernents can be reasonably understood. Based on the bonding chacter revealed in the electronic stntcture, we suggest that CaHz doped with a monovalent element could be a superconductor.