Based on the α-particle model of ~(12)C nucleus,the differential cross sections for α-~(12)C elastic scattering atincident energy of 4.2 GeV have been calculated within the framework of Glauber multiple scattering theory.The resultsshow that the main features of the measured angular distribution of the cross sections can be reasonably described.Theparameterized α-α scattering amplitude,which is the basic input to construct the α-~(12)C scattering Glauber amplitudein the α-particle model,is obtained by fitting the α-α scattering data. Based on the α-particle model of (12) C nucleus, the differential cross sections for α ~ (12) C elastic scattering atincident energy of 4.2 GeV have been calculated within the framework of Glauber multiple scattering theory. Result result that that the main features of the measured angular distribution of the cross sections can be reasonably described. Theparameterizedα-α scattering amplitude, which is the basic input to construct the α- 12 C scattering Glauber amplitudein the α-particle model, is obtained by fitting the α -α scattering data.