We proposed a Raman and erbium-doped fiber amplifiers (EDFA) hybrid bidirectional optical amplifier (HBOA). The hybrid amplifier consists of a fiber Raman amplifier (FRA) and two EDFA, which are ingeniously combined by four WDMs. Gain and noise figure (NF) are the metrics used to evaluate the performance. The effects of Raman and EDFA pump on the gain and NF of the proposed hybrid amplifier are explored, resulting in a maximum gain exceeding 40 dB and an NF below 0 dB. Furthermore, when the input signal power is small (−35 dBm), the proposed hybrid amplifier, exhibits a total gain increased of ∼14 dB, and NF reduction of ∼4 dB across the wavelength span of 1545 to 1565 nm, as compared with EDFA-only. Finally, The Allan deviation can reach 1.41×10−14 when HBOA was used, significantly better than the stability of 2.62×10−14 obtained by Bi-EDFA, which confirmed the feasibility of the proposed amplifier for radio frequency synchronization systems.