Aiming at the problem of resource auction mechanism in cloud environment， a more General multi-unit FAlse-name-proof auction mechanism for vIrTual macHine allocation （GFAITH） was studied and designed. First， the system model was formally defined. Then， around the design goals of being truthfulness and false-name-proof， it was proved that when considering the diversity of user demands， a new form of cheating， Demand-Reduction （DR） cheating， would emerge， which could destroy the truthful and false-name-proof properties， and the experimental results show that it would seriously affect the system performance. Based on the above， the GFAITH was proposed to achieve the design goals in three stages： user pre-processing， pre-allocation and pricing， and resisting demand reduction cheating. It is theoretical proved that the resource allocation of GFAITH is feasible and able to resist false-name-proof. Experimental results show that GFAITH can effectively guarantee the performance of the system from indicators such as revenue and social wealth， verifying the effectiveness and efficiency of the proposed mechanism.