The characteristics of distributed Bragg reflector(DBR) cavity are analyzed. A narrow-linewidth single-frequency ytterbium-doped fiber DBR laser is fabricated. The laser is pumped by a semiconductor laser operated at 977 nm. Its output power reaches 4 mW and the lasing linewidth is less than 8 MHz (instrument resolution limited) at free wavelength of 1052.5 nm. Up to 20.4 nm(1036.1-1056.5 nm) continuous tuning is demonstrated from this DBR fiber laser operating in single longitudinal mode using a simple beam bending tuning technique for axial extension and compression. Over the full tuning range, threshold pump power and slope efficiency vary with laser wavelength.