We studied on the magnetic damping constants (α) for L1 0-FeNi and disordered FeNi employing three kinds of measurement methods. An L10-FeNi thin film exhibited high perpendicular magnetic anisotropy of 7.1 × 106 erg cm-3. At magnetic fields (H) lower than 2 kOe, α was estimated to be 0.091 ± 0.003. However, it was reduced down to 0.013 ± 0.001 with H, indicating that extrinsic contributions enhance α. The intrinsic α = 0.013 ± 0.001 was comparable to α = 0.009 ± 0.002 for the disordered FeNi. This suggests that L10-FeNi is a candidate achieving high magnetic anisotropy and low magnetization damping simultaneously.