Graphene is at the center of a significant research effort for ultrafast photonics due to its unique optical properties. Here, we demonstrated the generation of stretched and soliton femtosecond mode-locking pulses in an erbium doped fiber laser (EDFLs) by using graphene saturable absorber and managing the net cavity dispersion. The novelty of this work arises due to the simple fabrication of the graphene SA and the realization of two types of mode-locking pulse by manipulating the cavity dispersion. At total cavity dispersion of −0.028ps2, stretched pulses train was successfully obtained. The laser has a pulse width of 750fs at repetition rate of 35.1MHz and pulse energy of 0.054nJ at maximum output power of 1.9mW. By varying the net cavity dispersion so that the anomalous dispersion has been achieved with total dispersion of −0.3ps2, soliton mode locked pulse train was successfully obtained. The laser has a pulse width of 820fs at repetition rate of 11.5MHz and pulse energy of 0.42nJ at output power of 4.85mW. These results make the proposed EDFLs suitable for applications in optical communications, metrology, environmental sensing, and biomedical diagnostics.