The modification of Bernstein operators given by Aldaz, Kounchev and Render has been intensively studied in the recent years. In this paper we define a corresponding modification for the general class of Baskakov-type operators. All these operators preserve the constants and j-th monomial for a given natural number j. We prove a general result of Voronovskaja type (Theorem 2.1) for positive linear operators acting on the infinite interval [0,?) and use this theorem to prove a Voronovskaja-type theorem for the whole class of the modified Baskakov-type operators.