We show that the relative intensity noise (RIN) of a mode-locked fiber laser can be suppressed below a -140 dB/Hz level for the entire > 20 Hz offset frequency range by a proper combination of intra-cavity and extra-cavity optical bandpass filters. When a 12-nm-bandwidth intra-cavity filter and a 16-nm-bandwidth extra-cavity filter are employed for a polarization-maintaining-nonlinear-amplifying-loopmirror (PM-NALM)-based Er-fiber laser, the RIN spectrum level is suppressed by similar to 30 dB in the low offset frequency range. The resulting integrated rms RIN is only 0.0054% [1 Hz-1 MHz]-to our knowledge, one of the lowest integrated RIN performances for any mode-locked laser reported so far. Besides the simplicity, this double-filtering approach has an additional advantage: unlike active pump-laser feedback methods, it does not have any resonant peaks in the stabilized RIN spectrum. In addition to the RIN suppression, with intra-cavity bandpass filtering, the integrated rms timing jitter is also reduced from 7.29-fs (no-filter) to 2.95-fs (12-nm intra-cavity filter) [10 kHz-1 MHz] in the soliton PM-NALM laser. (C) 2017 Optical Society of America