Gilbert damping constants α of Co/Pd multilayers with various layered structures were estimated by time resolved magneto-optical Kerr effect. The [Co(tCo)/Pd(tPd)]6 multilayers exhibiting a perpendicular magnetic anisotropy (PMA) were prepared by dc magnetron sputtering on a Pd (1 nm)/Ta (30 nm)/oxidized Si substrate. The PMA of the multilayer having tCo/tPd=0.55 increased with decreasing the bilayer period, tCo+tPd, while all the multilayers showed almost the same α of 0.09. The same trend was seen for Co/Ni multilayers with a constant tCo/tNi, although the values of α are different, i.e., 0.035 for Co/Ni . From the estimation of the damping α of the multilayers with various tCo/tPd, the α was confirmed to be enhanced when the ratio tCo/tPd becomes lower than 0.8. Moreover, the linear relationship between the α and tPd/tCo was found. These results suggest that the damping α of both Co/Pd and Co/Ni multilayers are not closely correlated with their PMA, and mainly determined by the composition of the multilayers.