We demonstrate a robust and low-noise all-polarization-maintaining (PM) nonlinear-amplifying-loop-mirror (NALM) mode-locked Er-fiber laser based on a 3×3 coupler. Since the 3×3 coupler generates 120-deg phase bias, the 3×3 PM-NALM laser can easily acquire mode-locked state even without any additional phase biasing components. In our experiment, the initiation of mode-locking required at least 1.5 times less pump power compared to the similar-structured 2×2 PM-NALM laser. The minimum relative-intensity noise (RIN) level reaches -155 dB/Hz with an integrated rms RIN of 0.0022% [10 Hz-1 MHz], which corresponds to one of the lowest integrated relative intensity noise (RIN) from any free-running mode-locked lasers. The laser also features very robust operation against mechanical vibrations. Stable mode-locked operation is maintained for more than 60 min even in continuous 1.5 grms vibrations.