•A backward facing step and unique inlet shape are used in a micro combustors.•The non-premixed hydrogen/air combustors with catalyst segment are compared.•Key parameters affecting the performance of a non-premixed hydrogen/air combustors are summarized. In this work, a type of non-premixed hydrogen/air micro combustor is designed for the application of micro-thermophotovoltaic (MTPV) systems. The micro combustor is presented with a backward-facing step and unique inlet shape to enhance the mixing performance and flame stabilization. The combustion, flow, and heat transfer characteristics of non-premixed hydrogen/air combustion in micro combustors with/without catalyst segment are numerically investigated. The results indicate that the homogeneous reaction is obviously weakened in the catalytic combustor, but a higher and more uniform outer wall temperature is obtained, and the outer wall temperature difference can be decreased by up to 28%. The flow characteristics of gaseous mixture in the catalytic combustor are better than those in the non-catalytic combustor. When the inlet velocity is 10 m/s, the average flow velocity and pressure loss of the catalytic combustor are decreased by up to 5.6% and 250 Pa, respectively. Furthermore, the heat of reaction and total heat flux at the gas–solid interface of the catalytic combustor are obviously higher and lower than those of the non-catalytic combustor, and the outer wall heat loss ratio is increased by up to 0.59% when the inlet velocity is 10 m/s. All in all, it can be concluded that adopting catalytic combustion to the micro combustor is extremely suitable for the application of MTPV systems.