In this paper, the presence of Rhodium catalyst walls near the premixed counterflow methane-air flame into a plus-shaped channel is investigated. To simulate the flame structure, a time dependent numerical analysis is carried out. The impact of reaction time and equivalence-ratio, from lean to rich combustion, on the flame characteristics are analysed and compared in catalytic and non-catalytic conditions. It is shown that the average value of CH4 mass fraction over the whole volume of the proposed geometry at the presence of Rhodium catalyst is decreased for about 26% relative to non-catalytic case. The results also showed that at different values of equivalence ratio, the maximum temperature of catalytic combustion is about 6% more than non-catalytic scenario. It is also shown that by passing the time, between 0.003s to 0.006s, average CH4 mass fraction for both catalytic and non-catalytic cases grow rapidly rather than that of after 0.006s; and also after 0.012s the flames would be steady.