We searched for the 6α-condensed state in 24Mg by measuring the C12+12C scattering with the SAKRA Si detector array at Ecm=17.5–25.0 MeV. By using the invariant-mass method for the detected 3α particles, the inclusive cross sections for the C12+12C→12C(02+)+X and C12(31−)+X reactions were determined. In addition, the missing-mass spectroscopy was successfully utilized to determine the excitation energy of the residual C12 nucleus and the exclusive cross sections for the C12+12C→12C(02+)+12C(01+), C12(02+)+12C(21+), and C12(02+)+12C(02+) reactions. In both the inclusive C12(02+)+X channel and the exclusive C12(02+)+12C(01+) channel, the cross section peaked at Ecm=19.4 MeV, which correspond to the excitation energy of Ex=33.3 MeV in 24Mg. This 19.4-MeV state is a candidate for the 6α-condensed state because of the agreement of the excitation energy with the theoretical value and its decay property. In the exclusive C12(02+)+12C(02+) channel, a broad state was observed at Ecm=22.5 MeV, which correspond to the excitation energy of Ex=36.4 MeV in 24Mg. From the angular distribution of the differential cross section, the spin and parity of this 22.5-MeV state was assigned to be 4+. In addition, a 2+ state was suggested at the low-energy side of the 22.5-MeV state. Because their excitation energies are higher than the theoretical value of the 6α-condensed state, these states might be excited states of the 6α-condensed state such as the 22+ and 41+ states in C12.