Based on density functional theory (DFT), four different methods with the generalized gradient approximation (GGA) have been employed to investigate the structural and electronic properties of the four polymorphs (alpha center dot H2O, beta, gamma, and epsilon phases) of CL-20, which is a well-known high energy density compound (HEDC). The relaxed crystal structures compare well with experimental data. According to the constitution of the frontier energy bands and the Mulliken population analyses, the N-NO2 bond is predicted to be the trigger bond during thermolysis. The density of states (DOS) of alpha-CL-20 center dot H2O is somewhat different from those of the other three crystals for its inclusion of H2O molecules that contribute the frontier energy bands. The band gaps obtained from the four different methods are consistent with each other. According to the calculated values of band gaps, the sensitivity of the four polymorphs of CL-20 is predicted as epsilon < beta < gamma < alpha center dot H2O, which agrees well with the experimental result. The effects of hydrostatic compression on the most stable epsilon-CL-20 have also been investigated using the GGA-PBE method in the pressure range of 0-400 GPa. epsilon-CL-20 has anisotropic compressibility at low or high pressure. The band gap is found to decease with increasing pressure, showing the corresponding sensitivity increase. Based on the changes of the band gap and DOS with pressure, 400 GPa is considered to be the critical pressure for the insulator-metal phase transition.