We prepared a novel diluted magnetic semiconductor of GaFeAs grown on (001) GaAs substrates using molecular beam epitaxy (MBE). The low growth temperature of the buffered GaAs layers is a key factor necessary for the creation of GaFeAs epilayers, without the anomalous nucleation of Fe atoms. The maximum Fe concentration of 1.5 x 10(21) cm(-3), which is the highest reported value, was successfully doped uniformly in GaAs. The 1 x 1-reflection high-energy electron diffraction patterns, indicating a well-ordered flat surface, were maintained during the growth of GaFeAs. X-Ray diffraction measurements showed that the peak shifted toward the higher angle side with an increasing Fe content in GaAs, implying that Fe atoms substitutionally occupy the GaAs lattice sites. Magnetization measurements revealed that the GaFeAs epilayers were predominantly paramagnetic, and that 5% of the total Fe atoms were segregated in the MBE-grown GaFeAs epilayers.