The inclusive transverse momentum (pT) distributions of primary charged particles are measured in the pseudo-rapidity range |η|<0.8 as a function of event centrality in Pb--Pb collisions at √sNN=2.76 TeV with ALICE at the LHC. The data are presented in the pT range 0.15<pT<50 GeV/c for nine centrality intervals from 70--80% to 0--5%. The Pb-Pb spectra are presented in terms of the nuclear modification factor RAA using a pp reference spectrum measured at the same collision energy. We observe that the suppression of high-pT particles strongly depends on event centrality. In central collisions (0-5%) the yield is most suppressed with RAA≈0.13 at pT=6-7 GeV/c. Above pT=7 GeV/c, there is a significant rise in the nuclear modification factor, which reaches RAA≈0.4 for pT>30 GeV/c. In peripheral collisions (70-80%), the suppression is weaker with RAA≈0.7 almost independently of pT. The measured nuclear modification factors are compared to other measurements and model calculations.