Ab initio molecular dynamics simulations were used to study the decomposition mechanism of 2, 4, 6, 8, 10, 12-hexanitro-2, 4, 6, 8, 10, 12-hexaazaisowurtzitane(CL-20) crystal, an excellent high energy density cage compound, under extreme conditions. It is found that the initiation and subsequent decomposition mechanisms of the CL-20 crystal are diverse at different conditions, and CL-20 is sensitive to both high temperature and pressure. Comparing the numbers of corresponding main products, it is found that the high pressure decelerates the decomposition. While, the appearance of special intermediates R-C_xO_y (x>2, y>5) indicates that the high pressure makes the decomposition much more complex. Among these intermediates, C₃O₆ is proved to be a high energy density compound.