The stimulated Raman scattering (SRS) in a multi-kilowatt co-pumping fiber amplifier was investigated. Using 20 m of ytterbium-doped double-cladding fiber in the amplifier stage, an SRS product of 1032.9 nm could be clearly observed when the output laser power was more than 3360 W. By integrating the spectral curve, the ratios of laser power at 1080 nm and SRS to the total output power were 83.95% and 15.17% at the maximum power of 3699 W. In addition, the beam quality began to degenerate abruptly as the four-wave mixing and SRS components appeared. The M-2 factor was measured to be 3.06 at the maximal output power. The mode instability and nonlinear effects might be the main reason for beam quality degradation in high-power fiber amplifier systems.