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.