In this paper by taking the cast heating PBX based on HMX as research object, the construction of hypothesized model of fragment acceleration of explosive explosion was established and the relationship of explosion heat and fragment velocity was discussed. The experimental verification was realized by the design of explosive formula with different Al content of several particle sizes and testing of several items including fragment velocity, penetration percentage, explosion velocity and explosion heat. The results indicated that the mathematical extreme value relationship between fragment velocity and explosion heat was existed, while the fragment velocity and penetration percentage shows the trend of increasing and then decreasing with increasing of Al/O ration and explosion heat. The fragment acceleration was best when the Al/O ratio and explosion heat was 0.35 and 6 200 kJ/kg respectively, indicating that fragment velocity and penetration percentage was maximized of 1 890 m/s and 89% which verifies the mathematical extreme value and optimal matching engineering point of the relationship between fragment velocity and explosion heat.