We perform density functional based calculations on the structures and stabilities of ZnFn clusters up to n = 6. We find that Zn can bind successively to four F atoms, expanding its oxidation state to +4 from nominal value of +2. All these species are stable in their neutral as well as anionic states. Furthermore, the adiabatic electron affinities of these species suggest that ZnFn behave as superhalogen for n > 2. Thus it may be possible, at least theoretically, to synthesize new class of compounds having predetermined oxidizing power utilizing ZnFn superhalogen clusters.