We consider the operators introduced in [V. Gupta, N. Ispir, On the Bezier variant of generalized Kantorovich type Balazs operators, Appl. Math. Lett. 18 (9) (2005) 1053-1061] and estimate their rate of convergence for absolutely continuous functions having a derivative coinciding a.e. with a function of bounded variation. (C) 2006 Elsevier Ltd. All rights reserved.