A 974 nm laser diode pumped 1120 nm ytterbium (Yb)-doped fiber laser with all fiber components has been experimentally demonstrated. The resonator is composed of a normal single-mode Yb-doped fiber 1 m long and a pair of fiber Bragg gratings. Up to 21.6 mW of continuous-wave output power is generated when the launched pump power is 161 mW with an optical-to-optical conversion efficiency of 13.4%. The central wavelength is 1120.89 nm with a linewidth as narrow as 0.02 nm. Additionally, a similar fiber laser with a 2 m long gain medium displays a broadened linewidth. The results of the two fiber lasers are compared and discussed in the paper.