We have performed ab initio molecular dynamics simulations to study coupling effects of temperature (534-873 K) and pressure (1-20 GPa) on the initiation mechanisms and subsequent chemical decompositions of nitramine explosive 1,3,5,7-tetranitro-1,3,5,7-tetrazocane (HMX). A new initiation decomposition mechanism of HMX was found to be the unimolecular C-H bond breaking, and this mechanism was independent of the coupling effects of different temperatures and pressures. The formed hydrogen radicals could promote subsequent decompositions of HMX. Subsequent decompositions were very sensitive to the pressure at low temperatures (534 and 608 K), while the temperature became the foremost factor that affected the decomposition at a high temperature (873 K) instead of the pressure. Our study may provide a new insight into understanding the coupling effects of the temperature and pressure on the initiation decomposition mechanisms of nitramine explosives.