Angular dependence of Gilbert's damping constant alpha for Ni-Fe(001) single-crystal thin films were investigated by employing Q-band (35 GHz) and X-band (9 GHz) ferromagnetic resonance analysis in terms of the specimen's crystal structure. The alpha for 10-nm-thick specimen had constant values of 0.006, which were estimated by the Q-band ferromagnetic resonance (FMR) spectra, when the spectra were measured with changing external field directions in the film plane and out of plane. The alpha for the Ni-Fe specimens did not depend on the crystal directions. The alpha values estimated by X-band FMR spectra were in good agreement with those by Q-band FMR spectra, when the magnetization of the specimens was saturated at the X-band resonance field. The alpha values were overestimated, when the magnetization was not saturated and the specimens had multidomain structures at the resonance field.