We have studied the structure of Au-6 cluster supported on acidic form of faujasite zeolite using density functional theory. In the gas phase Au-6 minimizes to a triangular structure while on zeolite support it has a three-dimensional structure with three apical centers bending towards the support. The hydrogenated clusters Au6H/(2H)-FAU, Au6H2/H-FAU and Au6H3/FAU generated by stepwise reverse hydrogen spillover from bridging OH groups of zeolite are energetically preferred over the Au-6/(3H)-FAU structure. The calculated reverse hydrogen spillover energy per hydrogen atom for zeolite supported Au6H, Au6H2 and Au6H3 clusters are -67.6, -65.6 and -59.1 kJ/mol, respectively.