Low phase noise mode-locked fiber laser finds important applications in telecommunication, ultrafast sciences, material science, and biology, etc. In this paper, two types of carbon nano-materials, i.e. single-wall carbon nanotube (SWNT) and graphene oxide (GO), are investigated as efficient saturable absorbers (SAs) to achieve low phase noise mode-locked fiber lasers. Various properties of these wall-paper SAs, such as saturable intensity, optical absorption and degree of purity, are found to be key factors determining the performance of the ultrafast pulses. Reduced-noise femtosecond fiber lasers based on such carbon-based SAs are experimentally demonstrated, for which the phase noise has been reduced by more than 10 dB for SWNT SAs and 8 dB for GO SAs at 10 kHz. To the best of our knowledge, this is the first investigation on the relationship between different carbon material based SAs and the phase noise of mode-locked lasers. This work paves the way to generate high-quality low phase noise ultrashort pulses in passively mode-locked fiber lasers.