CO adsorption on the polar (1[combining macron]1[combining macron]1[combining macron]) surface of the intermetallic compound GaPd is examined within ab initio methods using an all-electron full-potential electronic structure approach. Comparison between the PW-LDA, GGA-PBE, GGA-RPBE, GGA-revPBE, and hybrid HSE06 functionals is considered through bulk, clean surface and CO adsorption calculations. The choice of the functional is found to have a strong influence in the description of single CO adsorption on the surface model proposed in literature. As expected from the so called "CO adsorption puzzle", differences in the obtained results demonstrate that classic LDA and PBE functionals can only partially describe the complex CO adsorption bonding scenario on a surface containing transition metal elements (in this case Pd atoms), where the energies of the substrate-adsorbate electronic states are shifted, yielding important differences in the absolute values of the adsorption energies, vibrational frequencies and surface-adsorbate interaction. So far the hybrid functional HSE06 correctly retrieves all the tendencies observed experimentally as confirmed by comparing our first-principles results to experimental findings.