In order to predict the detonation initiations accurately with less computational effort, a reduced method was proposed to establish a three-step ethylene/air global reaction mechanism for detonation combustors. The activation energy of the three-step mechanism was set as a key parameter that varies with the initial state of the reactants. A database of detonation simulation activation energy was established in a range of the equivalence ratio of 0.7–2.3 and the pressure ahead of the precursor shock front of 0.2–2.0 atm. Compared with existing simplified chemical reaction mechanisms, the proposed mechanism was confirmed to better reproduce the results of GRI-Mech3.0 within the given applicability range. The developed mechanism was used to predict the lean and rich limits of detonation initiation for simulation successfully in an air-breathing pulse detonation combustor. The simulation results were consistent with the theoretical limits estimated by the detonation cell sizes. Stable operation of an air-breathing detonation combustor was achieved in the experiments. Moreover, a series of equivalence ratio ranges of detonation initiation and the initiation distances were obtained. The simulated limits fell within the two experimentally obtained ranges of the lean limit and the rich limit. This proved that the established three-step mechanism is appropriate for the simulations of detonation initiation.