Effect of wall thermal conductivity on hydrogen self-ignition and hydrogen-assisted ignition of propane-air mixtures in different feeding modes from ambient cold-start conditions were investigated numerically with chemical kinetic model in Pt/γ-Al2O3 catalytic micro-combustors. For the steady and transient state, effect of wall thermal conductivity on self-ignition characteristics of lean hydrogen-air mixtures was presented, and hydrogenassisted combustion of propane-air mixtures was investigated numerically in the co-feed mode and the sequential feed mode. The computational results indicate the large thermal inertia of the micro-combustor solid structure leads to slow temperature dynamics, and transient response is dominated by the thermal inertia. The heat localization in poorly conducting walls leads to fast ignition and shorter steady state time. In general, the concentration of hydrogen required for propane ignition increased with increasing wall thermal conductivity, decreasing inlet velocity, and decreasing inlet equivalence ratio of propane-air mixtures. In the co-feed mode, the combustion characteristics of hydrogen-assisted propane qualitatively resemble the selectively preheating initial portion of the combustion chamber wall. In the sequential feed mode, the time taken to reach steady state, the hydrogen cut-off time, the propane ignition time and the cumulative propane emissions increased with increasing wall thermal conductivity; the ignition characteristics are similar to partially preheating the initial segment for low and moderate wall thermal conductivity values (0.5 and 20 W/m·K); however, the ignition characteristics are close to completely heating the micro-combustor wall for high wall thermal conductivity values (200 W/m·K).