The concept of the generalized Perron complement concerning a nonnegative irreducible matrix was proposed by L. Z. Lu in 2002, and it was used to construct an algorithm for estimating the boundary of the spectral radius. In this study, we consider the properties of generalized Perron complements of nonnegative irreducible and diagonally dominant matrices. Moreover, we analyze the closure property of the generalized Perron complements of nonnegative irreducible $H$-matrices under certain conditions.