Abstract: We discussed a class of centralizer of the general linear Lie superalgebra by using homological method. Firstly, the general linear Lie superalgebras were divided into three cases for structural analysis, namely, gl(m,n),gl(m,0) and gl(0,n), where m and n were not zero. Secondly, the centralizers of the even and odd situation of the three cases in the generalized Witt Lie superalgebras were calculated respectively. Finally, the structure of this kind of centralizer was given.

Key words: centralizer, Lie superalgebra, zero cohomology group