In this study, we consider the bivariate complex q-Balazs-Szabados operators of the tensor product kind. Approximation properties of these operators attached to analytic functions on compact polydisks are investigated by using the results in the univariate case obtained for q-Balazs-Szabados operators in (Ispir and Yildiz Ozkan in J. Inequal. Appl. 2013: 361, 2013). In this sense, the upper estimate, the Voronovskaja-type theorem, and the lower estimate are obtained. The exact degree of its approximation is also given.