Based on the critical tube diameter and detonation cell size data in H₂-O₂/Air mixtures, the piston work done model was used to predict their critical energies of direct initiation. The good agreement is found by comparing the theoretical predicted critical energies with those measured in the experiment. Thus, the theoretical model is proved to be able to predict the critical energy of H₂-O₂/Air mixtures within satisfactory. From the theoretical prediction model, it is obviously shown that the critical energy for H₂-Air is significantly bigger than H₂-O₂ mixture when at the same initial conditions. The ZND induction zone length was further investigated to study the large critical energy discrepancy behavior between those mixtures, the results clearly indicated that the induction zone length for H₂-Air is much longer than that of H₂-O₂ mixture at the same initial condition, and it is cube relationship between critical energy and induction zone length, which results in the bigger critical energy of the H₂-Air mixture. This result is in agreement with the critical energy predicted from theoretical model.