A stable mode-locked fiber laser (MLFL) employing multi-layer graphene as saturable absorber (SA) is presented. The multi-layer graphene were grown by chemical vapor deposition (CVD) on Ni close to A-A stacking. Linear absorbance spectrum of multi-layer graphene was observed without absorption peak from 400 to 2000 nm. Optical nonlinearities of different atomic-layers (7-, 11-, 14-, and 21- layers) graphene based SA are investigated and compared. The results found that the thicker 21-layer graphene based SA exhibited a smaller modulation depth (MD) value of 2.93% due to more available density of states in the band structure of multi-layer graphene and favored SA nonlinearity. A stable MLFL of 21-layer graphene based SA showed a pulsewidth of 432.47 fs, a bandwidth of 6.16 nm, and a time-bandwidth product (TBP) of 0.323 at fundamental soliton-like operation. This study demonstrates that the atomic-layer structure of graphene from CVD process may provide a reliable graphene based SA for stable soliton-like pulse formation of the MLFL.