The structure of a topological space may be described by associating with it an algebraic system usually a group or a sequence of groups. There are several methods by which groups can be associated with topological spaces. Here we shall consider one through homotopy and the group so defined is called Fundamental group of the given topological space. The algebraic structure of the group reflects the topological and geometrical structures of the underlying space. The theory of Covering spaces is closely connected with the study of Fundamental group. Many basic topological questions about covering spaces can be reduced to purely algebraic questions about the fundamental groups of the various spaces involved. In Abstract Algebra, the action of a group on a set has many applications. We shall apply the group action concept of Abstract Algebra in Algebraic Topology. In this article we give description about the action of Fundamental group on Fibre set.