According　to　saturable　absorber　function　of　two-level　system　and　theoretical　model　of　Q-switched　mode　locking,　and　combining　with　all-solid-state　Yb:YAG　laser,　the　characteristics　of　the　saturable　absorption　of　graphene　which　is　varied　with　layers　and　the　critical　pump　power　of　Q-switched　mode　locking　have　been　studied　numerically.　It　can　be　seen　that　the　saturable　fluence　and　modulation　depth　are　proportional　to　the　graphene　layers.　The　critical　pump　power　will　decrease　when　the　graphene　layers,　transmittance　of　output　mirror,　beam　radius　on　graphene　and　cavity　length　decrease,　and　Q-switched　mode　locking　becomes　easier.　The　resonant　beam　radius　and　laser　crystal　length　have　an　optimal　value　each,　which　can　obtain　minimum　critical　pump　power.