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A stable narrow bandwidth semiconductor saturable absorber mirror mode-locked Yb-doped fiber laser was demonstrated in a short linear cavity with fundamental repetition rate up to 843 MHz. At the fundamental repetition rate of 490 MHz, the maximum output power was 17 mW at ~ 300-mW incident pump power. The center wavelength and the spectral bandwidth were 1064.1 and 0.13 nm, respectively, imposed by a narrow bandwidth fiber Bragg grating. The pulsewidth was measured to be 21 ps, and the time-bandwidth product of the laser pulse was 0.72.