1,3,5,7-Tetranitro-1,3,5,7-tetraazacyclooctane(HMX) is one of the most powerful and widely used explosives. A new method for the synthesis of HMX from 3,7-dipropionyl-1,3,5,7-tetraazabicyclo[3.3.1]nonane (DPPT) was investigated. Two important intermediates, 1,5-dipropionyl-3-nitroso-7-nitro-1,3,5,7-tetraazacyclooctane (DPNNO) and 1,5-dipropionyl-3,7-dinitro-1,3,5,7-tetraazacyclooctane (DPDN), were isolated from the reaction mixture. The reaction mechanism, involving a nitrolysis-nitrosolysis-nitrolysis-nitrolysis process, was proposed and verified by the H-1-NMR tracking. Based on the reaction mechanism, a stepwise method to prepare HMX from DPPT was developed. DPPT could be efficiently and smoothly converted to DPNNO in red fuming nitric acid with excellent yield up to 94.2 %. The influence factors on the yields of HMX such as reaction temperature, loading amounts of N2O5 were investigated. Under the optimized conditions, HMX was obtained with a satisfactory yield of 85.0 %. The overall yield of the stepwise procedure was as high as 80.0 %.