A mesoscale diverging combustor with a cylindrical flame holder is developed to improve the flame stabilization in present work for the first time. The experimental results show that the flame in the combustor with holder can remain symmetrically stable within a quite wide range of equivalence ratio. Then, the flame- anchoring mechanisms are analyzed systematically in terms of flow structure, conjugate heat exchange and preferential transport effect via numerical simulation. As the flame root and top attach to the flame holder and combustor, it can be deduced that the flow boundary layer very near the wall has the anchoring effect on the flame, so does the conjugate heat exchange. On the one hand, the upstream flame holder and combustor wall can preheat the incoming unburned mixture via conducting heat from the downstream solid walls, which provides a beneficial ignition condition. On the other hand, there are flame- wall coupling effects between the flame root/top and flame holder/combustor wall providing the suitable locations for flame anchoring. The anchoring locations of flame root and top show the almost same sensibility responding to the thermal conductivity of solid material. However, the anchoring temperature of flame top is more sensitive than that of flame root. In addition, the local equivalence ratios at the locations of the flame root and top are lower than the corresponding incoming equivalence ratio, which means that a better heat recirculation effect is not good for the flame- anchoring if only considering the preferential transport effect. In summary, the addition of flame holder can remarkably improve the flame stabilization and suppress the unstable flame in the combustor. This is beneficial for the application of the combustor with the diverging structure.