The supermode noise suppressing ratio (SMSR) and the phase noise of a harmonically mode-locked Erbium-doped fiber laser (HML-EDFL) with an intra-cavity semiconductor optical amplifier (SOA) and an optical band-pass filter (OBPF) are improved and compared with a state-of-the-art Fabry-Perot laser diode (FPLD) injection-mode-locked EDFL. By driving the intra-cavity SOA based high-pass filter at unitary gain condition, the SMSR of the HML-EDFL is enhanced to 82 dB at the cost of degrading phase noise, increasing jitter, and broadened pulse width. The adding of OBPF further improves the SMSR, pulse width, phase noise, and jitter of the SOA-filtered HML-EDFL to 90 dB, 42 ps, -112 dBc/Hz, and 0.7 ps, respectively. The ultrahigh SMSR of the SOA-filtered HML-EDFL can compete with that of the FPLD injection-mode-locked EDFL without sacrificing its pulse width and jitter performances.