Agrawal et al. (2015) constructed a bivariate generalization of a new kind of Kantorovich-type q-Bernstein-Schurer operators and studied a Voronovskaja type theorem and the rate of convergence in terms of the Lipschitz class function and the complete modulus of continuity. The concern of this paper is to obtain the degree of approximation for these bivariate operators in terms of the partial moduli of continuity and the Peetre's K-functional. Finally, we construct the GBS (Generalized Boolean Sum) operators of bivariate q-Bernstein-Schurer-Kantorovich type and estimate the rate of convergence for these operators with the help of mixed modulus of smoothness. © 2015 Published by ElsevierInc.