This paper is aimed at constructing new modified Gamma operators using the second central moment of the classic Gamma operators. And we will compute the first, second, fourth, and sixth order central moments by the moment computation formulas, and their quantitative properties are researched. Then, the global results are established in certain weighted spaces and the direct results including the Voronovskaya-type asymptotic formula, and point-wise estimates are investigated. Also, weighted approximation of these operators is discussed. Finally, the quantitative Voronovskaya-type asymptotic formula and Grüss Voronovskaya-type approximation are presented.
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