J/ψ production in pp collisions and in Pb-Pb collisions at the LHC with the ALICE experiment

We report the recent measurements of the inclusive J/ψ production in pp collisions at s=2.76TeV, in pp collisions at s=7TeV and in Pb-Pb collisions at sNN=2.76TeV with the ALICE detector at the LHC. The J/ψ mesons are detected down to pT=0GeV/c via their di-muon decay channel at forward rapidity (2.5