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The transverse momentum (pT) spectrum and nuclear modification factor (RAA) of reconstructed jets in 0-10% and 10-30% central Pb-Pb collisions at sNN−−−√=2.76 TeV were measured. Jets were reconstructed from charged and neutral particles, utilizing the ALICE tracking detectors and Electromagnetic Calorimeter (EMCal), with the anti-kT jet algorithm with a resolution parameter of R=0.2. The jet pT spectra are reported in the pseudorapidity interval of |ηjet|<0.5 for 40<pT,jet<120 GeV/c in 0-10% and for 30<pT,jet<100 GeV/c in 10-30% collisions. Reconstructed jets were required to contain a leading charged particle with pT>5 GeV/c to suppress jets constructed from the combinatorial background in Pb-Pb collisions. The effect of the leading charged particle requirement has been studied in both pp and Pb-Pb collisions and has been shown to have negligible effects on the RAA within the uncertainties of the measurement. The nuclear modification factor is obtained by dividing the jet spectrum measured in Pb-Pb by that in pp collisions scaled by the number of independent nucleon-nucleon collisions estimated using a Glauber model. RAA is found to be 0.28±0.04 in 0-10% and 0.35±0.04 in 10-30% collisions, independent of pT,jet within the uncertainties of the measurement. The observed suppression is in fair agreement with expectations from two model calculations with different approaches to jet quenching.