Micro-combustion is a promising technology for addressing global energy consumption challenges; however, its practical implementation is hindered by a limited understanding of the underlying reaction characteristics. To address this, a comprehensive numerical investigation was conducted using a well-established two-dimensional (2D) steady model to examine the influence of key operating parameters (e.g., inlet velocity, equivalence ratio, and inlet temperature) on catalytic methane/air combustion in micro-channels. The results show that the heterogeneous reaction exhibits limited sensitivity to changes in inlet velocity, whereas the homogeneous reaction shows substantial enhancement with increasing inlet temperature. With the increment of inlet velocity, the peak value of stage III- heterogeneous ignition (conversion of CO to CO2 and H2 to H2O) decreases and levels off once uin ≥ 0.50 m/s. Simultaneously, the minimum value of S (the ratio of heat released by the heterogeneous reaction to that of the total reaction) decreases as well. As the equivalence ratio is increased, the combustion zone shifts towards the upstream direction. The value of S initially increases and then decreases, reaching a maximum of 17.61 % at Φ = 0.95. Raising the inlet temperature results in the upstream movement of the flame, accompanied by reduced combustion heat release, lower combustion temperature, and diminished intensity of homogeneous combustion. The influence of the heterogeneous reaction on combustion is more pronounced under operating conditions with lower inlet velocities, an equivalence ratio approaching 0.95, and higher inlet temperature. Additionally, under the condition of higher inlet velocities, an equivalence ratio close to 1.0, and elevated inlet temperature, the heterogeneous reaction aids in igniting the homogeneous reaction more effectively.