In order to balance the suppression of stimulated Raman scattering (SRS) and transverse mode instability (TMI) in high-power fiber lasers, in this letter, a new type of spindle-shaped YDF with asymmetric longitude distribution was designed and produced which had small-size input end, large-size transmission section and moderate output end enabling fitting well with seed laser and mitigating SRS as well as TMI effects. A counter-pumped fiber laser amplifier was established using this YDF and two kinds of laser diodes (LDs) were adopted for increasing TMI threshold. Finally, the maximum output power reached 6 kW and the beam quality (M2 factors) indicates near-single-mode output. The SRS suppression ratio under 6 kW output power was 36 dB and no dynamic TMI was observed which reveals that further enhancement of output power was just limited by pump power.