A fiber phase noise suppression system is built. By out-of-loop self-beat frequency, the noise floor of 6.8×10-18 is obtained in the average time of 1 s, and it falls down to 2.3×10-19 after the average time of 2000 s. The laser frequency with narrow linewidth is transferred in a 1.6 km fiber link when we use the proposed system, and the frequency stability of out-of-loop self-beat frequency signal is 1.2×10-17 in the average time of 1 s. Based on the 808 m fiber link which connects the two laboratories, the laser linewidth of (0.54±0.15) Hz and the frequency stability of 1.2×10-15 in average time of 1 s can be obtained in beat frequency measurement when we apply the proposed system to the comparison of 1.5 μm ultra-stable laser systems.