We report on a tapered large-core Yb fiber laser operating at 976 nm emission wavelength. It was realized using a high-numerical aperture large-core fiber with 126 µm core diameter, which was fabricated by powder sinter technology and shows a very homogeneous step index profile. The end of the fiber is tapered down to match a single mode fiber containing a Fiber Bragg Grating. Using the benefits of core pumping and the feedback of the spliced Fiber Bragg Grating, we achieved efficient pump light absorption and wavelength stable 976 nm lasing with single-mode performance. We could demonstrate 10 W laser power out of a 10 µm fiber core with a slope efficiency of 31% with respect to the launched pump power. The presented device is well-suited for fiber coupled pumping of amplifiers for high peak power.