A stable single-frequency fiber ring laser with linewidth less than 0.5 kHz is presented,in which the self-written fiber grating induced by saturable absorption inner an unpumped Er3+ doped fiber at the standing-wave section is applied. Its power is more than 1 dBm and the lasting time of no mode-hopping is more than 3 hours. The RF spectra were measured by the homodyne method,when the mode-hopping occured.