In this paper, we established a high power tandem pumped fiber amplifier based on tapered ytterbium-doped fiber (TYDF). The TYDF is developed in-house with a core/inner cladding diameter of 30/250 µm at the small-core region and 48/400 µm at the large-core region. The key parameters of the amplifier in a co-pumped and counter-pumped configuration are experimentally investigated, such as slope efficiency, stimulated Raman scattering (SRS) threshold, and beam quality evolution. Up to 10.28 kW laser free of SRS or transverse mode instability is obtained from the counter-pumped amplifier, and the beam quality factor M2 is 2.29, which is significantly improved compared with the 48/400 µm uniform YDF. To the best of our knowledge, this is the highest average output power achieved so far based on the TYDF. This work could provide a solution for balancing the SRS suppression and high order modes control in high power tandem pumped YDF lasers.