The production of prompt charmed mesons D0, D+ and D*+, and their antiparticles, was measured with the ALICE detector in Pb-Pb collisions at the centre-of-mass energy per nucleon pair, √sNN of 2.76 TeV. The production yields for rapidity |y|<0.5 are presented as a function of transverse momentum, p_T, in the interval 1-36 GeV/c for the centrality class 0-10% and in the interval 1-16 GeV/c for the centrality class 30-50%. The nuclear modification factor R_AA was computed using a proton-proton reference at Vs = 2.76 TeV, based on measurements at Vs = 7 TeV and on theoretical calculations. A maximum suppression by a factor of 5-6 with respect to binary-scaled pp yields is observed for the most central collisions at p_T of about 10 GeV/c. A suppression by a factor of about 2-3 persists at the highest p_T covered by the measurements. At low p_T (1-3 GeV/c), the R_AA has large uncertainties that span the range 0.35 (factor of about 3 suppression) to 1 (no suppression). In all p_T intervals, the R_AA is larger in the 30-50% centrality class compared to central collisions. The D-meson R_AA is also compared with that of charged pions and, at large p_T, charged hadrons, and with model calculations.
