The transverse momentum ($p_{\rm T}$) spectrum and nuclear modification factor ($R_{\rm AA}$) of reconstructed jets in 0-10% and 10-30% central Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV were measured. Jets were reconstructed from charged and neutral particles, utilizing the ALICE tracking detectors and Electromagnetic Calorimeter (EMCal), with the anti-$k_{\rm T}$ jet algorithm with a resolution parameter of R=0.2. The jet $p_{\rm T}$ spectra are reported in the pseudorapidity interval of $|{\eta}_{\rm jet}|< 0.5$ for $40< p_{\rm T,jet}< 120$ GeV/$c$ in 0-10% and for $30< p_{\rm T,jet}< 100$ GeV/$c$ in 10-30% collisions. Reconstructed jets were required to contain a leading charged particle with $p_{\rm T}>5$ 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 $R_{\rm AA}$ 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. $R_{\rm AA}$ is found to be $0.28\pm0.04$ in 0-10% and $0.35\pm0.04$ in 10-30% collisions, independent of $p_{\rm T,jet}$ 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.