The Haus master equation which describes the laser dynamics is solved numerically so as to study the effects of cavity parameters and characteristics of graphene saturable absorber on the pulses characteristics. Adopting the fast saturable absorber model, the relations between pulse characteristics with cavity length, graphene layers, transmittances of output mirror and beam radius on the laser medium are analyzed. In addition, the results are compared with that of semiconductor saturable absorption miror (SESAM). The conclusions show that the graphene and SESAM have different advantages. For example, for higher pulse energy, graphene is favorable for shorter cavity length and smaller radius on saturable absorber, while the SESAM is better for the opposite situation. The saturable absorbers and cavity parameters should be chosen properly according to concrete situations.