A single-frequency distributed Bragg reflector (DBR) fiber laser at 1030 nm has been demonstrated using a 0.7 cm long homemade Yb:YAG crystal-derived silica fiber (YCDSF). The absorption and emission cross sections of the YCDSF are $4.93\times {10}^{-20}{\mathrm{cm}}^2$ at 980 nm and $1.1\times {10}^{-20}{\mathrm{cm}}^2$ at 1030 nm. Using this gain fiber, an over 255 mW continuous-wave lasing in the constructed laser has been obtained at single transverse and longitudinal mode operation. The slope efficiency and the pump threshold of the fiber laser were up to ～35% and as low as 25 mW, respectively. The fiber laser also demonstrated an optical signal-to-noise ratio of 79 dB and a beam quality factor of 1.016 in two orthogonal directions. Its power fluctuation at 210.5 mW was less than 0.85% of the average power within 13 h. Moreover, the relative intensity noise and linewidth of the laser are also investigated at the different pump powers. The results indicate that the single-frequency DBR fiber laser has potential applications in high-quality seed sources and high-precision optical sensing.