We have successfully compressed the pulse duration of an all-normal-dispersion (ANDi) Yb-fiber laser to sub-100 fs by a single-mode nonlinear fiber amplifier. Through optimizing the input power, prechirp, and the pump power of the amplifier, the pulse duration of the ANDi Yb-fiber laser is compressed to 68 fs when a 2.5-m active fiber is used, although for a 3.5-m active fiber, the pulse duration of the laser can be compressed to 58 fs. We have also shown that a low relative intensity noise is maintained within the nonlinear amplification process. The experimental results prove this ultrashort-pulse-duration and low-noise laser source with moderate output power can be a good candidate for frequency comb, multiphoton imaging, coherent Raman spectroscopy, and other applications.