Abstract Gilbert's damping constants, α, of Co( t Co)/Pt (1.4 nm) multilayer thin films are investigated by Q-band FMR analysis. α is calculated from the resonance width of the FMR spectrum. With decreasing t Co, the α value decreases from 0.034 ( t Co=8.7 nm) to 0.023 ( t Co=1.8 nm), and then increases to 0.037 ( t Co=1.0 nm). The decrease of α with t Co>1.8 nm is probably due to the eddy current loss effects. The increase of α with t Co<1.8 nm would be caused by the increase of the distortion between the Co and the Pt layers at the interface. When the magnetic field direction was changed from θ=90° (parallel to the specimen) to θ=0° (perpendicular to the specimen), the α of all the specimens increased, and a sharp step in α was observed around θ=40°, where the α has the maximum value.