Based on the model of ytterbium-doped fiber amplifier and the effect of the central wavelength of the amplifier and the length of gain fiber on amplified spontaneous emission (ASE) is analyzed. According to the calculation results, the 1030 nm narrow linewidth fiber laser amplifier is optimized. Adopting the structure of master oscillator power amplifier (MOPA), a continuous wave (CW) laser with central wavelength of 1030 nm, 3 dB linewidth of 0.072 nm and maximum power of 1.01 kW is achieved with narrow band seed and one stage amplifier, in which 25 μm/400 μm (diameters of core/cladding) ytterbium-doped fiber is used as the gain fiber. The optical-to-optical conversion efficiency is 81%, and 1030 nm output power is more than 99% of total output power. The calculated and experimental results show that by reasonable optimization design, 1030 nm narrow linewidth CW fiber amplifier with high power, high efficiency and high signal noise ratio can be achieved.