The purpose of this paper is to introduce a Kantorovich variant of Lupas-Stancu operators based on Polya distribution with Pochhammer k-symbol. We obtain rates of convergence for these operators by means of the classical modulus of continuity. Also, we give a Voronovskaja type theorem for the pointwise approximation. Furthermore, we construct a bivariate generalization of these operators and we discuss some convergence properties of them. Finally, we present some figures to compare approximation properties of our new operators with those of other operators which are mentioned in this paper. We observe that the approximation of our operators to the function f is better than that of some other operators in a certain range of values of k.