  We consider a leptophobic Z^\prime scenario in a flipped SU(5) grand unified
theory obtained from heterotic string theory. We show that the allowed Z^\prime
mass, flavor conserving and flavor changing couplings of the Z^\prime to the
down-type quarks are strongly constrained by the mass difference in
B_s-\bar{B}_s system and the four branching ratios of B -> \pi K decays. It is
shown that even under these constraints large deviations in direct and/or
indirect CP asymmetries of B \to \pi K decays from the SM expectations are
allowed. Especially it is possible to accommodate the apparent puzzling data in
B -> \pi K CP asymmetries.
