  We discuss nonanomalous R-symmetry in the supersymmetric grand unified
theories. In particular, we explore anomaly-free solutions predicting the
gravitino mass in the range of $10^{-3} eV \lsim m_{3/2} \lsim 1 TeV$ when the
$\mu$-parameter is fixed to be $\mu \simeq 1 TeV$. In the minimal SU(5) GUT, we
have shown that $\mu \simeq 1 TeV$ is obtained only if the gravitino is
ultralight with mass $m_{3/2} \sim 10^{-3} eV$. If extra fields ${\bf
5}\oplus{\bf 5^*}$ or ${\bf 10}\oplus{\bf 10^*}$ are introduced, many solutions
predicting $m_{3/2} \gsim 10^{-3} eV$ are found. The R-parity is violated due
to the vacuum expectation value of the superpotential, but it is controlled by
the discrete R-symmetry. We find that the R-parity violating couplings are
naturally suppressed much below the experimental bounds for some charge
assignments. These charge assignments predict light gravitino with masses of
order ${\cal O}(10^{-3} eV)$--${\cal O}(1 MeV)$. These discrete R-symmetries
can be considered as solutions to the $\mu$-problem in low energy supersymmetry
breaking models such as the gauge mediation.
