In this work, a large-mode-area (LMA) step-index constant-cladding tapered-core (CCTC) Yb-doped fiber with a cladding diameter of ∼600 µm is successfully fabricated. The CCTC fiber has a small-core region (diameter of ∼20 µm) at both ends and a large-core region (diameter of ∼36 µm) in the middle. To prove the laser performance of the CCTC fiber, a detailed comparison experiment with conventional uniform fiber with the same effective core diameter is carried out in a multi-kW all-fiber MOPA configuration. The experimental results show that employing the CCTC fiber can effectively mitigate the thermally-induced transverse mode instability (TMI) in both co-pump and counter-pump schemes, and realize high slope efficiency and single-mode beam quality (M 2 ∼1.30). Under the counter-pump scheme, the TMI threshold of the CCTC fiber is observed at ∼2.49 kW with a slope efficiency of 86.2%, while the uniform fiber amplifier exhibits a TMI threshold of ∼2.05 kW. The theoretical analysis based on a semi-analytical model indicates this CCTC fiber can effectively improve the TMI threshold owing to a stronger gain saturation. Our results verify the great potential of such an LMA CCTC fiber to mitigate thermal-induced TMI effect and achieve single-mode operation without sacrifice of laser efficiency in high power monolithic fiber lasers, and the further power scaling is expected by optimizing the fiber design.