A novel linear cavity single-frequency erbium doped fiber laser,in which a fiber Bragg grating(FBG) provides external feedback,was numerical modeled.Robust and no mode hopping single-frequency operation in this laser can be achieved.Furthermore,the longer the external cavity length is,the narrower the linewidth of the laser.The single-frequency working space of the laser has also been achieved.In order to obtain higher output power of single-frequency signal and maximally utilize the surplus pump energy,a section of 3.3 m Er~(3+)-doped fiber was added to the output end.The output power is 0.373 mW that is increased by 7 dB than that without amplification.The slope efficiency is about 0.75 %.