Focusing on the Ni80Fe20 (Py)/Nd-Cu bilayers, the magnetization dynamic damping from spin pumping effect is investigated systematically by doping itinerant Cu in rear earth metal Nd. Various Ta/Py/Nd1-xCux/Ta/Si films with x = 0%, 16%, 38%, 46% and 58% are prepared by magnetron sputtering. For every content of Cu, the thickness of Nd-Cu layer is changed from 1 nm to 32 nm. The damping coefficient increases with increasing the thickness of Nd-Cu layer, which shows the trend of the spin pumping behavior. Also, with increasing Cu concentration in the Nd-Cu layer, the damping coefficient decreases, implying that the spin-orbit coupling in Nd-Cu layer is indeed cut down by high itinerant of Cu dopants. It is interesting that the spin diffusion length (λSD) in the Nd-Cu layer for different Cu dopants is not found to increase monotonously.