Polarized inelastic neutron-scattering experiments have been performed to elucidate the anisotropic behavior of the low-energy spin-wave excitations in a multiferroic BiFeO3, which shows a cycloidal spin structure below 640 K. Using neutron polarization analysis for single magnetic domain crystals, magnetic excitation modes in and out of the cycloidal plane below 6 meV were separated successfully. The magnetic excitation spectra were analyzed using linear spin-wave theory. The low-energy magnon density of states consist of several magnon modes, including the two anisotropic modes, Φ and Ψ modes, distributed in and out of the cycloidal plane, respectively, which were previously observed using optical spectroscopies. Furthermore, there are other magnon modes that are not active in optical measurements. A model spin Hamiltonian, which reproduces the spin-wave frequencies observed using optical spectroscopies, explains the overall spectra reasonably well.