  We study a torus-like compactification of type IIB maximally supersymmetric
PP-wave background. As the most general case, we discuss a T^8 compactification
of all the transverse directions. A nontrivial structure of the isometry group
requires an additional light-like compactification. This additional S^1 fiber
is twisted on the T^8. We determine the spectrum of closed strings in this
twisted torus background and compute the thermal partition function.
