  We propose the hybrid gravity-gauge mediated supersymmetry breaking where the
gravitino mass is about several GeV. The strong constraints on supersymmetry
viable parameter space from the CMS and ATLAS experiments at the LHC can be
relaxed due to the heavy colored supersymmetric particles, and it is consistent
with null results in the dark matter (DM) direct search experiments such as
XENON100. In particular, the possible maximal flavor and CP violations from the
relatively small gravity mediation may naturally account for the recent LHCb
anomaly. In addition, because the gravitino mass is around the asymmetric DM
mass, we propose the asymmetric origin of the gravitino relic density and solve
the cosmological coincident problem on the DM and baryon densities \Omega_{\rm
DM}:\Omega_{B}\approx 5:1. The gravitino relic density arises from asymmetric
metastable particle (AMP) late decay. However, we show that there is no AMP
candidate in the minimal supersymmetric Standard Model (SM) due to the robust
gaugino/Higgsino mediated wash-out effects. Interestingly, AMP can be realized
in the well motivated supersymmetric SMs with vector-like particles or
continuous U(1)_R symmetry. Especially, the lightest CP-even Higgs boson mass
can be lifted in the supersymmetric SMs with vector-like particles.
