In order to achieve a larger amplification bandwidth, while increasing the output gain and maintaining a small gain flatness, a second-order Raman fiber amplifier is designed, which used a second-order pump and four first-order pumps to perform distributed Raman amplification on 100 channels of signal light. First, numerically solve the second-order Raman coupled wave equation. Simultaneously, in order to further improve the output performance, the performance parameters of the second-order Raman fiber amplifier are optimized by using particle swarm optimization algorithm. Then, under the same pump parameter configuration, compare the first-order RFA with the second-order RFA. Finally, the factors affecting the output gain of the second-order Raman amplifier are analyzed. Through experimental simulation, within the 1 510~1 610 nm gain bandwidth range, the designed second-order Raman fiber amplifier has an average output gain of 23.768 0 dB, a maximum output gain of 24.124 4 dB and the gain flatness is 0.911 2 dB.