This work gives the experimental verification about the existence of the 11.528 MeV state in 24Mg which was newly discovered with the recoil-coincident technique in HI reaction. Resonant γ-ray absorption method has been used. Several dips have been observed in the resonance absorption transmission curve and recognized to be the fine structure around the 11.528 MeV excited energy level. The excitation energy and level width were deduced for each sub-level and the total width of energy level 13.321 MeV in emitting nucleus 28Si was also obtained from data fitting procedures.