In this paper, we present a novel single-mode Yb-doped fiber with 14 µm core and 45 µm cladding diameter. A 976 nm all-fiber high-power amplifier was manufactured based on this fiber. 10-mm-long fiber taper was used to launch the pump light, and guidance of the high NA pump was provided by a glass-air interface. 13 W output power limited only by the available pump power was achieved with 31% slope efficiency.