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A compact single-mode distributed Bragg reflector (DBR) fiber laser with narrow spectral linewidth is investigated. Firstly, based on our theoretical analysis the single longitudinal mode operation domain is obtained. Then, a single-mode DBR fiber laser of 7.9cm long with master oscillator power amplifier (MOPA) configuration is designed and constructed to operate in the single-mode domain. The fiber laser is pumped by a semiconductor laser at 975.5nm. The master oscillator operates at 1556.91 nm with a cw output power of 1.43mW for a pump power of 55.35 mW. Its slope efficiency is 2.7% and the spectral linewidth is less than 1.2MHz (instrument resolution limited). With the MOPA configuration the laser output power and slope efficiency are increased to 7.8mW and 16.9%, respectively.