This paper studies a dual-wavelength single-frequency Er-doped fiber laser based on ring cavity, the output wavelengths are 1 570 nm and 1 548 nm. The laser combines Fabry-Perot (FP) filter and Fiber Bragg Grating (FBG) to achieve wavelength selection and preliminary stabilization. And two unpumped Er-doped fibers act as saturable absorbers to realize linewidth narrowing effect. The Laser Diode (LD) used has a maximum drive current of 700 mA, which corresponds to a maximum pumping power of 450 mW and 500 mW. When the pump power of LD1 is up to 58 mW and the diver current of LD2 is up to 138 mW, the fiber laser gets dual-wavelength output. The output power of the 1 570 nm and 1 548 nm laser generated at this time are 4.2 mW and 10.1 mW respectively. Then the pump power of LD1 and LD2 are adjusted to 104 mW and 83 mW respectively, and the output laser characteristics were studied under this condition. The output power in 1 570 nm is 10.3 mW, and the Optical Signal to Noise Ratio (OSNR) is 58 dB. The output power in 1 548 nm is 4.7 mW, and the OSNR is 55 dB. It shows that the output laser has a relatively high-quality factor and high slope efficiency. Then the stability of the output laser is studied. In order to measure the stability of the output laser of the dual-wavelength single-frequency laser, data collection is started half an hour after the laser is turned on in the experiment. Every 10 min, the spectrum is collected and the output power is recorded. The power fluctuations of the laser output in 1 570 nm and 1 548 nm are 0.01 dBm and 0.02 dBm, respectively, and the wavelength drifts of the output laser are both less than 0.01 nm. The result shows that the fiber laser can avoid the mutual interference between the two wavelengths. The output laser has good power stability and wavelength stability. The laser linewidth is the parameter of most concern for a single-frequency fiber laser. In this experiment, the linewidths of the output laser are measured by the delay non-zero self-heterodyne method based on the Mach-Zehnder interferometer and fitted with the Lorentz curve. And it can be calculated from the -20 dB bandwidth of the Lorentz curve. The linewidths of output laser in 1 570 nm and 1 548 nm measured are about 230.2 Hz and 223.6 Hz. The narrow linewidth indicates that the output laser has good single-frequency performance, and it is also an important basis for the wide application of this laser. In this study, the idea of multiplexing Fiber Fabry-Perot (FFP) filter is proposed, and the two sub-cavities do not interfere with each other by introducing circulator at both ends of FFP. It also does not introduce any expensive polarization devices, and does not need to use a polarization controller to control the polarization state of the light in the cavity. So it greatly reduces the difficulty of experimental operation and cost of the experiment. The fiber laser has a simple structure, good stability and the output laser has a narrow linewidth. It provides a technical method for realizing dual-wavelength single-frequency laser output, and it can also be used as a seed light source in high precision measurement field.