We show in this paper a time-dependent (TD) quantum wave packet calculation for the combustion reaction H+O-2 using the DMBE IV (double many-body expansion) potential energy surface which has a deep well and supports long-lived resonances. The reaction probabilities from the initial states of H+O-2((3) Sigma(g)(-)) (v=0-3, j=1) for total angular momentum J=0 are obtained for scattering energies from threshold up to 2.5 eV, which show numerous resonance features. Our results show that, by carrying out the wave packet propagation to several picoseconds, one can resolve essentially all the resonance features for this reaction. The present TD results are in good agreement with other time-independent calculations. A particular advantage of the time-dependent approach to this reaction is that resonance structures-strong energy dependence of the reaction probability-can be mapped out in a single wave packet propagation without having to repeat scattering calculations for hundreds of energies. We also report calculations of some low-lying vibrational energies of the hydroperoxyl radical HO2((2)A") and their spectroscopic assignments. The vibrational frequencies of HO2((2)A") on the DMBE IV potential energy surface are lower than experimental values, indicating the need to further improve the accuracy of the potential energy surface.