An L-band single-longitudinal-mode (SLM) erbium-doped fiber laser (EDFL) is proposed and experimentally demonstrated to exhibit an ultranarrow linewidth and a high optical signal-to-noise ratio. A multistage filter, which is composed of a thin film filter, a fiber Bragg grating, and a saturation absorption, is utilized as an effective mode-selecting filter to achieve an SLM EDFL. The SLM EDFL with an ultranarrow linewidth of 205 Hz is obtained at the measurement resolution bandwidth of 100 Hz. In addition, the stability performance of the EDFL is measured during 30 min. The maximum fluctuations of the center wavelength and the output power of the proposed EDFL are 0.04 nm and 0.01 dB.