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The remarkable evolution of ytterbium-doped fiber (YDF) lasers and amplifiers is interrupted by a limiting thermo-optical effect called transverse mode instability (TMI). Hereon, we propose a Gaussian-shaped gain-dopant distributed (GSGDD) YDF, which is fabricated by a modified chemical vapor deposition (MCVD) process combined with solution doping technique (SDT). By regulating the solution concentrations of soot layers, the content of Yb^3+ ions presents Gaussian-shaped distribution in the transverse direction while the refractive index profile (RIP) exhibits a stepped profile. The laser performance of this fiber is verified by a bidirectional pumped master oscillator power amplifier (MOPA). Over 3 kW near-single-mode laser output is obtained with the slope efficiency of 84.9%. At the highest power output, there are no Stokes light components in the spectrum and the beam quality M² factor is ∼1.45 These results suggest that the GSGDD fiber owns great potential to achieve high power output with excellent beam quality.