We have developed a couple of optimal damping algorithms (ODAs) for unrestricted Hartree-Fock (UHF) calculations of open-shell molecular systems. A series of equations were derived for both concurrent and alternate constructions of α and β Fock matrices in the integral-direct self-consistent-field (SCF) procedure. Several test calculations were performed to check the convergence behaviors. It was shown that the concurrent algorithm provides better performance than does the alternate one.