In this study, we consider statistical approximation properties of univariate and bivariate λ-Kantorovich operators. We estimate rate of weighted A-statistical convergence and prove a Voronovskaja-type approximation theorem by a family of linear operators using the notion of weighted A-statistical convergence. We give some estimates for differences of λ-Bernstein and λ-Durrmeyer, and λ-Bernstein and λ-Kantorovich operators. We establish a Voronovskaja-type approximation theorem by weighted A-statistical convergence for the bivariate case,