The utilization of the exhaust gas of a solid oxide fuel cell is important to improve the energy efficiency and control pollutant emission. In this work, the combustion of solid oxide fuel cell exhaust gas (H2/CO) in a honeycomb ceramic catalytic burner is investigated numerically. A 2D numerical combustion model with 17 channels is built to analyze the influence of channel position on thermal performance and combustion characteristics. The high burnout of H2 and CO is obtained as 96.75% and 97.75%, respectively. The channels can be divided into three groups from the inside to the outside as follows: part 1, from the 9th channel to the 13th channel; part 2, from the 14th channel to the 16th channel; and part 3, the 17th channel. The channels in the same group presented the same results of flow, temperature, and combustion. Compared with the other channels, the outermost channel shows notable differences in depressing the temperature of the whole channel, moving the maximum temperature downstream, enlarging the temperature bias of the lower and upper walls, and enlarging the combustion zone. H2 and CO perform different combustion processes in the honeycomb ceramic catalytic burner. Compared with H2, the initial position of CO conversion is more affected by channel distribution. In the 17th channel, the CO oxidation rate is controlled mostly by the slower oxygen adsorption and the resulting low O(s) coverage. In the 9th channel, the CO oxidation rate is controlled mostly by the wall temperature and fuel-limited. The burnout rate of H2 changes from 95% to 99.9% with the channel position, but the burnout of CO varies little. The closer the channel to the outer wall, the higher the proportion of heterogeneous reaction and the more the generated heat. The generated heat by the channel can present a diversity of 4%.