Studies on the abilities of different density functional methods applied to hydrogen-bonded complexes have been carried out on the water-carbon monoxide complex. Various local and nonlocal exchange-correlation functionals have been used in the investigation of the structure, energetics, and vibrational properties of the 1:1 complex. A triple-zeta basis set, added with diffuse functions and multiple sets of polarization functions (e.g., 6-311++G(2d,2p)), has been used throughout the study. The comparison with the experimental data from the molecular beam measurements and also the results from previous ab initio calculations (second-order Moller-Plesset perturbation theory and coupled cluster with the single, double, and triple excitations) shows good performance of the complex energetics and structural parameters. Especially the hybrid methods mixing the Hartree-Fock exchange with DFT exchange-correlation present their strength for the description of hydrogen-bonded complexes. Additionally, the hybrid methods give good approximations for the vibrational shifts upon complexation comparable to the recent experimental matrix isolation results for the two stable complex structures H2O-CO and H2O-OC.