Local parity-odd domains are theorized to form inside a Quark-Gluon-Plasma (QGP) which has been produced in high-energy heavy-ion collisions. The local parity-odd domains manifest themselves as charge separation along the magnetic field axis via the chiral magnetic effect (CME). The experimental observation of charge separation has previously been reported for heavy-ion collisions at the top RHIC energies. In this paper, we present the results of the beam-energy dependence of the charge correlations in Au+Au collisions at midrapidity for center-of-mass energies of 7.7, 11.5, 19.6, 27, 39 and 62.4 GeV from the STAR experiment. After background subtraction, the signal gradually reduces with decreased beam energy, and tends to vanish by 7.7 GeV. The implications of these results for the CME will be discussed.