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We present a simple and stable single-longitudinal-mode (SLM) erbium-doped fiber laser. It consists of an apodized fiber Bragg grating (FBG) and a high finesse FBG-based Fabry-Perot (FP) etalon in the ring cavity. The apodized FBG acts as a wavelength discriminative component selecting a few oscillation modes while the FP etalon serves as narrow bandwidth bandpass filter to further discriminate and select SLM efficiently. Stable SLM laser output at 1.55 m with linewidth about 2.5 kHz is acquired. Furthermore, continuous wavelength tuning over 8 nm is achieved by simultaneously applying strain to the FBG and the FP etalon.