An over 75 nm broadband spectrum with a gain per unit length of >2 dB/cm was obtained from a homemade Yb: YAG crystal-derived silica fiber (YCDSF) with Yb-doping concertation of 6.57 wt.%. Using a 13-cm-long YCDSF, a low-noise wavelength-tunable single-frequency fiber laser has been constructed, enabling a single longitudinal mode oscillation from 1009 to 1070 nm. In particular, in the 1023-1056 nm waveband, the laser operating at any wavelength exhibited a maximum output power over 37 mW with power fluctuations below 0.38%, a slope efficiency >8%, and an optical signal-to-noise ratio higher than 60 dB. A linewidth of less than 2.8 kHz was also observed at the maximum pump powers, and relative intensity noise was as low as -155 dB/Hz at frequencies above 1.0 MHz. These results indicate that the YCDSFs with broadband high-gain characteristics are promising for wavelength-tunable fiber lasers in applications such as optical coherence tomography, precision metrology, nonlinear frequency conversion, and so on.