  This paper gives a necessary and sufficient condition for Gorensteinness in
Rees algebras of the $d$-th power of parameter ideals in certain Noetherian
local rings of dimension $d\ge 2$. The main result of this paper produces many
Gorenstein Rees algebras over non-Cohen-Macaulay local rings. For example, the
Rees algebra $\mathcal{R}(\mathfrak{q}^d)=\oplus_{i\ge 0}\mathfrak{q}^{di}$ is
Gorenstein for every parameter ideal $\mathfrak{q}$ that is a reduction of the
maximal ideal in a $d$-dimensional Buchsbaum local ring of depth 1 and
multiplicity 2.
