The precessional magnetization dynamics of high quality epitaxial magnetite (Fe3O4) thin films growth on MgO are investigated by inductive magnetization dynamic measurements in time and frequency domain. An upper bound for the intrinsic Gilbert damping parameter of alpha(0) =0.037 +/- 0.001 is derived, which is significantly lower than previously reported for epitaxial Fe3O4 on GaAs. With increasing film thickness from 5 up to 100 nm a strong increase in the effective damping up to 0.2 is observed which cannot be explained by simple nonuniform spin wave excitations. Possible origins of this effect are discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3531989] ; PUBLISHED ; SFI