By carrying out first-principles calculations on diamond-forming processes, we predict a method for the heteroepitaxial growth of diamond on cubic beta-SiC(001). In the method, we used two processes: (i) the preformation of an sp(3)-like surface configuration of beta-SiC(001) by the adsorption of group-V surfactants; (ii) the successive growth of diamond by the segregation of the surfactants onto a surface and the desorption of surface hydrogen. Analyzing the segregation energies, we found that the atomic size effect plays a crucial role in the surfactant-mediated growth of diamond on beta-SiC(001).