In order to test a possible evolutionary scenario of high-z compact quiescent galaxies(cQGs)that they can survive as local compact cores embedded in local massive galaxies with different morphology classes,we explore the star formation histories of local compact cores according to their spectral analysis.We build a sample of 182 massive galaxies with compact cores(M*,core > 1010.6 M⊙)at 0.02 ≤ z ≤ 0.06 from SDSS DR7 spectroscopic catalogue.The STARLIGHT package is used to analyze the median stacked spectra and derive the stellar ages and metallicities.Our main results show that local compact cores have the average age of about 12.1± 0.6 Gyr,indicating their early formation at z > 3,which is consistent with the formation redshifts of cQGs at 1 < z 80％)will evolve into local massive early-type galaxies according to dry minor merger,while some of them(～ 15％)will build substantial stellar/gas discs according to the late-time gas accretion and sustaining star formation,and finally grow up into spiral galaxies.