The crossing number of a graph G, c r (G) , is defined as the smallest possible number of edge-crossings in a drawing of G in the plane. There are almost no results concerning crossing number of join of a disconnected 6-vertex graph with cycle. The main aim of this paper is to give the crossing number of the join product Q + C n for the disconnected 6-vertex graph Q consisting of the two 3-cycles, where C n is the cycle on n vertices. [ABSTRACT FROM AUTHOR]