  The $\mu\nu$SSM provides a solution to the $\mu$-problem of the MSSM and
explains the origin of neutrino masses by simply using right-handed neutrino
superfields. Given that R-parity is broken in this model, the gravitino is a
natural candidate for dark matter since its lifetime becomes much longer than
the age of the Universe. We consider the implications of gravitino dark matter
in the $\mu\nu$SSM, analyzing in particular the prospects for detecting gamma
rays from decaying gravitinos. If the gravitino explains the whole dark matter
component, a gravitino mass larger than 20 GeV is disfavored by the isotropic
diffuse photon background measurements. On the other hand, a gravitino with a
mass range between 0.1-20 GeV gives rise to a signal that might be observed by
the FERMI satellite. In this way important regions of the parameter space of
the $\mu\nu$SSM can be checked.
