If used dielectric film as cavity mirrors, the output laser linewidth of fiber laser would be wide, moreover the longitudinal mode frequency and output power are not stable enough because of the lack of effective mechanisms for frequency selection. Using fiber grating as laser cavity mirrors, we can acquire stable ,narrow linewidth laser output. Through the analysis of optical fiber bragg grating formation mechanism and the frequency selection principle of bragg grating, dual bragg fiber grating linear cavity theory are obtained. the length of the fiber brgg grating resonator and fiber bragg grating center wavelength meet*, fiber grating is more suitable than dielectric film as cavity mirror.(* Indicates a formula, please see the full text)