The 976 nm laser diodes are utilized to provide the bi-directional pumping sources for the fiber amplifier based on 20/400 μm gain fiber. The transverse mode instability and the stimulated Raman scattering (SRS) effects are effectively suppressed under the operation of optimizing the coiling bending of gain fiber, pumping method, and pumping power distribution. A 3 kW level all-fiber amplifier with near-single-mode output is finally achieved. The optical-to-optical efficiency is around 73%, the SRS rejection ratio is 20 dB, and the beam quality factor is below 1.7. There are no mode instability characteristics detected in the time/frequency domain. A continuous 10 h test of this amplifier is carried out and the results show that the amplifier is stable, and is possible for its application in areas such as industrial processes.