In the present paper, we introduce a Stancu type generalization of Szász-Durrmeyer operators including Brenke type polynomials. We give convergence properties of these operators via Korovkin's theorem and the order of convergence by using a classical approach. As an example, we consider a Stancu type generalization of the Durrmeyer type integral operators including Hermite polynomials of variance v. Then, we obtain the rates of convergence by using the second modulus of continuity. Also, for these operators including Hermite polynomials of variance v, we present a Voronovskaja type theorem and r-th order generalization of these positive linear operators.