The performance of the unitary group approach (UGA) based coupled cluster singles and doubles (CCSD) method in application to van der Waals interactions involving high-spin open-shell systems is examined. The tested approach is fully spin-adapted in the sense that any intermediate quantity appearing in the formulation of the theory is free from spin contamination contributions. Interaction energies are computed within the supermolecular approach and corrected for the basis set superposition error. Several methods of solving UGA CCSD equations are used with the emphasis on iterative processes based on the Hamiltonian partitionings employed in the spin-restricted many-body perturbation theories. Test calculations are performed for the ground states of HeLi, H2Li, and for the excited a (3)Sigma(u)(+) state of Li-2. The UGA CCSD interaction energies are compared with those computed using the spin-unrestricted and valence universal coupled cluster methods, spin-restricted and spin-unrestricted many-body perturbation expansions, and the full configuration interaction method. The obtained results show that the UGA CCSD method performs very well in applications to weakly bound open-shell systems, giving results as good or better than other open-shell coupled cluster approaches.