Let the -Bernstein polynomials are given by
In this paper, a -analog of the Bleimann, Butzer and Hahn operators of the form
is proposed, where is a suitable positive linear isomorphism. The authors study the properties of the -BBH operators and establish the rate of convergence. A Voronovskaja-type theorem and saturation of convergence for -BBH operators for is discussed. Further, the convergence of the derivative of -BBH operators is considered.