In this article, we concentrate on the Szász-Jakimovski-Leviatan operators imposed by Appell polynomials using q-calculus. We analyze the classical Szász-Jakimovski-Leviatan-Kantorovich and derive the approximation results connected to the non-negative parameters ς ∈ [ 1 2 , ∞) in q-analogue. In order to combining with the earlier investigation by utilizing the Korovkin's theorem we study the local as well as global approximation theorems in terms of uniform modulus of continuity of order one and two. We calculate the rate of convergence by using of Lipschitz-maximal functions. Moreover, the Voronovskaja-type approximation theorem is also calculated here.