In order to balance the mitigation of transverse mode instability and stimulated Raman scattering effect in the high power fiber lasers, a specially designed Yb-doped fiber, named spindle-shaped Yb-doped fiber, was fabricated with a core/cladding diameter of 20/400 µm at both ends and 30/600 µm in the middle. Based on this fiber, an all-fiber laser oscillator was built and over 3 kW near-single-mode (M2 factor ∼1.3) laser was achieved with an optical-to-optical conversion efficiency of 78.4%. While operating at the maximum power, the transverse mode instability is well mitigated and the stimulated Raman scattering effect is well suppressed (>34dB lower than signal laser). Further power scaling is promising by optimizing the structure of the Yb-doped fiber.