Gilbert damping constants of Co/Pd multilayers with various layered structures were estimated by time resolved magneto-optical Kerr effect. The [Co(t(Co))/Pd(t(Pd))](8) 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 t(Co)/t(Pd) = 0.55 increased with decreasing the bilayer period, t(Co) + t(Pd), while all the multilayers showed almost the same of 0.09. The same trend was seen for Co/Ni multilayers with a constant, although the values of alpha are different, i. e., 0.035 for Co/Ni [9]. From the estimation of the damping of the multilayers with various t(Co)/t(Pd), the alpha was confirmed to be enhanced when the ratio becomes lower than 0.8. Moreover, the linear relationship between the alpha and t(Co)/t(Pd) was found. These results suggest that the damping of both Co/Pd and Co/Ni multilayers are not closely correlated with their PMA, and mainly determined by the composition of the multilayers.