•First application of a spindle-shaped gain fiber in a QCW fiber oscillator system.•Achieving the highest output peak power of near-single-mode QCW fiber lasers ever reported (peak power 6.4 kW, M2 factor 1.38).•Analyzed the causes of relatively low optical conversion efficiency and waveform deformation of QCW fiber laser. High peak power quasi-continuous wave (QCW) fiber lasers with good beam quality are widely used in industry. But it’s difficult to balance the peak power and the good beam quality for common lasers. We proposed a novel QCW fiber laser oscillator, employing a 24 m long spindle-shaped ytterbium-doped fiber (YDF), which has a core/cladding diameter of 25/400–37.5/600–25/400 μm. The large core diameter section in the middle and tapered sections are 20 m long in total for suppressing the nonlinear effects in the laser cavity, and the small core diameter sections in two ends are 4 m to result in good beam quality. Finally, a near-single-mode QCW fiber laser oscillator with a beam quality of 1.38 (M2 factor) and peak power of 6.4 kW is achieved, accompanying with a high stimulated Raman scattering (SRS) suppression ratio of 20.3 dB. To the best of our knowledge, this is the first time to adopt a spindle-shaped YDF in a QCW fiber laser, and also the highest output power of near-single-mode QCW fiber lasers ever reported.