A dominating set D is called a connected dominating set, if it induces a connected subgraph in G. Since a dominating set must contain atleast one vertex from every component of G, it follows that a connected dominating set for a graph G exists if and only if G is connected. The minimum of cardinalities of the connected dominating sets of G is called the connected domination number of G and is denoted by γc(G). We have defined new parameter called the matching dominating set and the matching domination number.We consider Kronecker product of two graphs, matching domination of product graphs and recall the results associated to the matching domination of Kronecker product of graphs. We prove the following: • In G1(k)G2 then deg(ui, vj ) = deg(ui).deg(vj ). • If G1 and G2 are finite graphs without isolated vertices then G1(K)G2 is a finite graph without isolated vertices. • |VG1(k)G2 | = |VG1 ||VG2 | • |EG1(k)G2 | = 2|EG1 ||VE2 | • If G1 and G2 are regular graphs, then G1(K)G2 is also a regular graph. • If G1 or G2 is a bipartite graph then Gl(k)G2 is a bipartite graph. • The matching domination number of c4(k)Km is 4. • If G1, G2 are two graphs without isolated vertices then γm[G1(k)G2] = γm(G1).γm(G2) where G1(k)G2, is the Kronecker product of graphs.