In heavy ion collisions at the LHC, the ALICE experiment is studying nuclear matter at very high energy density where the formation of a Quark Gluon Plasma (QGP) is expected. J/ψ production is an important probe to characterize the properties of the QGP as it gives access to the early stages of the collision. However a fundamental understanding of the J/ψ production mechanism in p-p collisions is important to study the nuclear matter effects on J/ψ production in Pb-Pb collisions. In 2010 and 2011, the LHC provided p-p collisions at √s = 7 and 2.76 TeV and Pb Pb collisions at √s = 2.76 TeV per nucleon pair. We will report on the latest measurements of J/ψ production at mid-rapidity (in the dielectron channel) and at forward rapidity (in the dimuon channel).