  We report on the $J/\psi$ production in Pb-Pb collisions at
$\sqrt{s_{NN}}=$2.76 TeV recorded with ALICE during the 2010 and 2011 LHC runs.
The $J/\psi$ candidates are reconstructed using the $e^{+}e^{-}$ and
$\mu^{+}\mu^{-}$ decay channels at mid- and forward rapidity, respectively. We
show the $J/\psi$ nuclear modification factor $R_{AA}$ as a function of
centrality, transverse momentum and rapidity. Our results are compared to the
lower energy measurements from PHENIX and to model calculations.
