In this paper we have obtained some novel generating functions of C + n n (x)-a modification of Gegenbauer polynomials, C n (x) by utilizing L. Wesiner's group-theoretic method. By giving suitable interpretations to both the index (n) and the parameter () of the polynomial under consideration, we obtain, in section 2, a set of infinitesimal operators known as raising and the lowering operators which generates a four dimensional Lie algebra. Finally, in Section 3, a novel generating function of the modified Gegenbauer polynomials which in turn yields a number of new and known results on generating functions