In this paper, Lupaş Bernstein-Kantorovich operators have been studied using Jackson and Riemann type (p, q)-integrals. It has been shown that (p, q)-integrals as well as Riemann type (p, q)-integrals are not well defined for 0 < q < p < 1 and thus further analysis is needed. Throughout the paper, the case 1 ≤ q < p < ∞ has been used. Advantages of using Riemann type (p, q)-integrals are discussed over general (p, q)-integrals. Lupaş Bernstein-Kantorovich operators constructed via Jackson integral need not be positive for every f ≥ 0. So to make these operators based on general (p, q)-integral positive, one need to con- sider strictly monotonically increasing functions, and to handle this situation Lupaş Bernstein-Kantorovich operators are constructed using Riemann type (p,q)-integrals. However Lupaş (p,q)-Bernstein-Kantorovich operators based on Riemann type (p, q)-integrals are always positive linear operators. Approximation properties for these operators based on Korovkin’s type approximation theorem are investigated. The rate of convergence via modulus of continuity and function f belonging to the Lipschitz class is computed.