We have systematically investigated the Gilbert damping constant α for L10-FePd films using the time-resolved magneto-optical Kerr effect (TRMOKE). The field angle dependence of TRMOKE signals was measured and analyzed. The field angle dependence of the lifetime of magnetization precession was explained by evaluating extrinsic contributions such as the anisotropy distribution and two-magnon scattering. The crystalline uniaxial perpendicular magnetic anisotropy constant Ku and α values were evaluated for FePd films for various L10 order parameters S. Ku values of approximately 15 Merg/cm3 were obtained for films with large-S values (i.e., over 0.8). In addition, α for the low-S film was found to be approximately 0.007 and decreased with increasing S. Smaller values of α (of 0.002-0.004) were obtained for films with S values of approximately 0.6-0.8. Results revealed that FePd films have both large-Ku and small-α values, which is a useful property for low-power magnetization switching while maintaining high thermal stability in spin-transfer-torque magnetoresistive random access memory applications.