The aim of this paper is to introduce the notion of c* generalized -closed sets in topological spaces and study their basic properties. It is the weaker form of closed and generalized c*-closed sets. Further, we shall see that the collection of c* generalized -closed sets is not closed under finite intersection but it is closed under arbitrary union. Also, we establish the relationship between this new class of closed sets with other existing classes of generalized closed sets in general topology. 2020 AMS Subject Classification: 54C08, 54C10, 54D10, 54D30.