To understand the metal-support interaction of oxide supported transition metal catalysts, we computed the reaction mechanisms of dry and steam reforming of methane on a tetragonal ZrO2(101) supported Ni catalyst. Based on the limited number of active sites on the surface, an irregular and non-ideal Ni13 cluster on ZrO2(101) is identified as a catalyst. A simple reaction mechanism is proposed, and the first direct dissociation step of CO2, CH4 and H2O is the most difficult based on the computed Gibbs free energies and no surface CHXO and CHXOH intermediates are involved, different from that on the flat Ni(111) surface. Analysis of other supported nickel catalysts shows that not only the support but also the size and shape of the metal clusters play an important role in the reaction mechanisms and kinetics.