Let G= ( V , E ) be a simple connected graph. A set S V is a total dominating set of G if every vertex is adjacent to an element of S. Let Dt(Wn ,i) be the family of all total dominating sets of the graph Wn , n ≥ 3 with cardinality i, and let dt (Wn ,i) = │Dt (Wn 2 , i) │. In this paper we compute dt(Wn ,i),and obtain the polynomial Dt(Wn , x) = dt(Wn 2 , i)x n+1 i=Υt (W n ) , which we call total domination polynomial of Wn , n ≥3 and obtain some properties of this polynomial.