We demonstrate a PM-NALM fiber laser utilizing a 3x3 coupler. While a 2x2 coupler causes no phase bias between counter-propagating lights in the NALM, the 3x3 coupler can generate a phase bias (2μ3) in the NALM without an additional nonreciprocal phase shifter. As a result, this 3x3 coupler-based NALM laser requires less than 2 times pump power for the mode-locking initiation compared to the 2x2 PM-NALM laser with a similar repetition-rate and configuration. The minimum rms relative-intensity-noise (RIN) is only 0.0048% integrated from 10 Hz to 1 MHz offset frequency, which is one of the lowest RINs demonstrated from free-running mode-locked lasers so far.