We give a new generalization of Bleimann, Butzer, and Hahn operators, which includes q-integers. We investigate uniform approximation of these new operators on some subspace of bounded and continuous functions. In Section 3, we show that the rates of convergence of the new operators in uniform norm are better than the classical ones. We also obtain a pointwise estimation in a general Lipschitz-type maximal function space. Finally, we de? fine a generalization of these new operators and study the uniform convergence of them. Copyright (C) 2007.