LetRbe a unit-regular ring , letXbe the set of all nonzero, nonunits ofRand letGbe the group of all units ofR. In this paper, some finiteness properties ofRare investigated by considering group actions ofGonXas follows:First, in case of half-transitive regualr action if 2 is unit inRor the number of idempotents inRis finite, thenRis finite. Secondly, ifGis cyclic and 2 is unit inR, then every orbit under regualr action is a finite set, and so in this case, ifRhas a finite number of idempotents, thenRis finite. Finally, ifFis a field in which 2 is unit and the multiplicative group of all nonzero elenents inFforms a cyclic group, thenFis finite.