Fiber-coupled semiconductor laser (LD)-pumped fiber laser amplifiers have the advantages of small size, high power-to-mass ratio, and good stability. However, limited by the level of device fabrication and the stimulated Raman scattering effect and mode instability (MI) effect inside the fiber, it is difficult for LD-pumped fiber laser amplifiers to achieve high-power and high-brightness laser output at the same time. To achieve higher power and higher brightness fiber laser output, it is necessary to combine the existing device technology and simultaneously realize effective suppression of the SRS and MI effect in the amplifier. Based on this, this paper reports the successful realization of 13 kW power and high beam quality laser output based on a homemade large-mode-area (LMA) gain fiber. The laser adopts the main oscillation power amplifier structure, and the LMA gain fiber is counter-pumped by 981 nm LDs in the amplification stage. When the total pump power is 15 kW, the output power reaches 12.94 kW, and the beam quality M² factor is about 2.85. By further optimizing the device performance and fiber mode control, it is expected to achieve higher power and higher brightness fiber laser output.