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A single-longitudinal-mode (SLM) dual-wavelength erbium-doped fiber (EDF) laser based on a simple linear cavity is proposed and demonstrated. The SLM operation is achieved by incorporating a dual-phase-shift fiber grating with two ultranarrow transmission bands. Due to the gain grating produced by spatial hole-burning in the EDF, the proposed linear cavity supports dual-wavelength oscillation at room temperature with a wavelength interval of 27 pm. The laser output is heterodyned on a photodetector and the generated microwave signal has a linewidth <20 kHz without any feedback.