The paper is devoted to establish new approximation properties of the well known Bernstein-Kantorovich operators. The main results of the paper are contained in Theorem 3.1,Theorem 3.2, Theorem 4.1 and Theorem 4.2,Where one proves that the Bernstein-Kantorovich operators have the ability of preserving translation property in both \(C\) and \(L ^p\) norms.