In this paper, from the viewpoints of both the first and the second law of thermodynamics, we conduct a comprehensive study on hydrogen-air counter-flow diffusion combustion in various modes. The effects of air inlet temperature (T-oxi) and effective equivalence ratio of fuel (phi) on the reaction zone structure and entropy generation of combustion are revealed over a wide range of T-oxi and phi. Through the present work, five interesting features of combustion of this kind, which are quite different from that reported in the literature, are presented. Especially, for the first time we divide various combustion modes in the phi - T-oxi map instead of the popular way used in previous studies. Such innovation can help judge the final combustion regime more straightforwardly for any given operative condition. Copyright (C) 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.