Lin (J. Inequal. Appl. 465, 2014 [10]) introduced a new modified Schurer-type q-Bernstein Kantorovich operators and discussed a local approximation theorem and the statistical convergence of these operators. In this paper we study the rate of convergence by means of the first-order modulus of continuity, Lipschitz class function, the modulus of continuity of the first-order derivative and the Voronovskaja-type theorem. © Springer India 2015.