The magnetic anisotropy energy and the resonance linewidth of epitaxial Fe3Si grown on GaAs(001) is studied by ferromagnetic resonance (FMR) technique. For a nearly stoichiometric sample (25.5% Si-content) a clear fourfold anisotropy is observed which is modulated by a small contribution of an uniaxial in-plane anisotropy. This uniaxial component is found to increase with the Fe concentration in the intermetallic compound. The samples show an exceptional narrow resonance linewidth of only 17 Oe at 9 GHz excitation frequency confirming the very high structural quality.