The graphene-polymer SA thin film using solution blending method and atomic layer graphene as saturable absorber (SA) used to generate femtosecond laser pulse were measured. Stable soliton-like pulses with the pulsewidth of 403 fs and 432 fs, the spectral linewidth of 6.32 nm and 6.16 nm, and the time-bandwidth product of 0.315 and 0.329 using graphene-PVA film and atomic layer graphene as SA were achieved, respectively, in mode-locked Er-doped fiber ring laser. The graphene-PVA SA suffered from larger loss caused by graphene flake aggregating, while the atomic layer graphene had smaller nonsaturable loss which exhibited lower mode locking threshold power. Atomic layer graphene also had stable fabricated process and controllable modulation depth depended on its layer numbers. To compare the mode locking performance of single wall carbon nanotubes (SWCNTs) and graphene SA, the same solution blending fabricated sample was used. Under similar nonsaturable loss and modulation depth, the SWCNTs SA with optimized concentration of 0.5wt% and thickness of 188£gm had shortest pulsewidth of 440 fs and 3-dB spectral linewidth of 6 nm. The shortest pulsewidth of 403 fs and broad spectral linewidth of 6.32 nm was obtained using graphene SA with concentration of 6.25wt% and thickness of 18£gm. Graphene has broad band absorbance and larger modulation depth, the experimental result indicates that graphene SA can generate shorter pulse and has chance to become the potential candidate of SA.