We demonstrate that the intrinsic properties of monolayer graphene allow it to act as a more effective saturable absorber for mode-locking fiber lasers when compared to multilayer graphene. The absorption of monolayer graphene can be saturated at lower excitation intensity compared to multilayer graphene, graphene with wrinkle-like defects, or functionalized graphene. Monolayer graphene has a remarkably large modulation depth of 65.9%, whereas the modulation depth of multilayer graphene is greatly reduced due to nonsaturable absorption and scattering loss. Picosecond ultrafast laser pulses (1.23 ps) can be generated using monolayer graphene as a saturable absorber. Due to the ultrafast relaxation time, larger modulation depth and lower scattering loss of monolayer graphene, it performs better than multilayer graphene in terms of pulse shaping ability, pulse stability, and output energy.