We report the experimental observation of collective picosecond magnetization dynamics in [Co/Pd]8 multilayers with perpendicular magnetic anisotropy. The precession frequency shows large and systematic variation from about 5 GHz to about 90 GHz with the decrease in the Co layer thickness from 1.0 to 0.22 nm due to the linear increase in the perpendicular magnetic anisotropy. The damping coefficient α is found to be inversely proportional to the Co layer thickness and a linear relation between the perpendicular magnetic anisotropy and α is established. We discuss the possible reasons behind the enhanced damping as the d-d hybridization at the interface and spin pumping. These observations are significant for the applications of these materials in spintronics and magnonic crystals. © 2011 American Institute of Physics.