A novel linear cavity erbium-doped fiber (EDF) laser based on a structured chirped fiber Bragg grating (CFBG) filter is proposed for stable single-polarization (SP) single-longitudinal-mode (SLM) operation. For the first time, to the best of our knowledge, a structured CFBG filter with an ultranarrow transmission band which is generated by tapering directly on CFBG is used to select the laser longitudinal mode. The SLM operation is obtained by using the structured CFBG together with an unpumped EDF acting as a saturable absorber. The fluctuations of the laser peak power and center wavelength are less than 0.07 dB and 1 pm in 1 h, respectively. The stable SP operation is achieved by using the inline broadband polarizer. The measured 20 dB laser linewidth is about 27.7 kHz, which indicates the laser linewidth is approximately 1.39 kHz FWHM.