A compact, low-noise, single-frequency fiber laser by using a newly developed ${\mathrm{Yb}}^{3+}$ heavily doped single-mode phosphate glass fiber has been demonstrated. Over $400\mathrm{mW}$ stable continuous wave single transverse and longitudinal mode laser at $1.06\mathrm{\mu m}$ was achieved from a $0.8\mathrm{cm}$ long active fiber. The measured slope efficiency and estimated quantum efficiency of laser emission are 72.7% and 93%, respectively. The signal-to-noise ratio is higher than $72\mathrm{dB}$ , and the linewidth of the fiber laser is less than $7\mathrm{kHz}$ , while the measured relative intensity noise is less than $-130\mathrm{dB}/\mathrm{Hz}$ at frequencies of over $1.5\mathrm{MHz}$ .