The 12C+12C fusion reaction is famous for its complication of molecular resonances, and plays an important role in both nuclear structure and astrophysics. It is extremely difficult to measure the cross sections of 12C+12C fusions at energies of astrophysical relevance due to very low reaction yields. To measure the complicated resonant structure existing in this important reaction, an efficient thick target method has been developed and applied for the first time at energies Ec.m.<5.3 MeV. A scan of the cross sections over a relatively wide range of energies can be carried out using only a single beam energy. The result of measurement at Ec.m.= 4.1 MeV is compared with other results from previous work. This method would be useful for searching potentially existing resonances of 12C+12C in the energy range 1 MeV<Ec.m.<3 MeV.
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