We report the recent measurements of the inclusive J/{\psi} production in pp
collisions at \sqrt{s} = 2.76 TeV, in pp collisions at \sqrt{s} = 7 TeV and in
Pb-Pb collisions at \sqrt{s_{NN}} = 2.76 TeV with the ALICE detector at the
LHC. The J/{\psi} mesons are detected down to pT = 0 GeV/c via their di-muon
decay channel at forward rapidity (2.5 < y < 4) and via their di-electron decay
channel at mid-rapidity (|y| < 0.9). A special emphasis is put on the nuclear
modification factor which is compared to the predictions of current J/{\psi}
production models
