We give a Kantorovich variant of a generalization of Szasz operators defined by means of the Brenke‐type polynomials and obtain convergence properties of these operators by using Korovkin′s theorem. We also present the order of convergence with the help of a classical approach, the second modulus of continuity, and Peetre′s K‐functional. Furthermore, an example of Kantorovich type of the operators including Gould‐Hopper polynomials is presented and Voronovskaya‐type result is given for these operators including Gould‐Hopper polynomials.