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We introduce a new q-parametric generalization of Bleimann, Butzer, and Hahn operators in C1+x*[0,∞). We study some properties of q-BBH operators and establish the rate of convergence for q-BBH operators. We discuss Voronovskaja-type theorem and saturation of convergence for q-BBH operators for arbitrary fixed 0<q<1. We give explicit formulas of Voronovskaja-type for the q-BBH operators for 0<q<1. Also, we study convergence of the derivative of q-BBH operators.