The amorphous zeolitic imidazolate frameworks (a-ZIFs) models and its analogues (with 918 or 810 atoms, respectively) are constructed based on a larger continuous random network (CRN) model of amorphous SiO2 (a-SiO2) model. The atomic, electronic, and dielectric properties of these structures, which possess different metal nodes and organic linkers, are investigated by well-defined density functional theory (DFT) calculations. The results suggest that all a-ZIFs have ultra-low dielectric constants and a large energy loss function (ELF), which suggests that they may be good candidates for electromagnetic absorptive materials. Most important, these a-ZIFs models offer a base-line model for other amorphous ZIFs for further research on models containing vacancies, defects, doping or under high pressure or high temperature.