A design passively Q-switched Nd:YAG microchip laser based on graphene saturable absorber is presented. A thin layer of graphene is sandwiched between the Nd:YAG crystal and YAG crystal closely, and dichroic coatings on crystals is used as reflective mirrors for the plane parallel resonator. The Nd:YAG crystal is end pumped by a fiber-coupled laser diode via a lens imaging system. Employing graphene as saturable absorber, Q-switched Nd:YAG microchip laser is realized at the pump power threshold of 1.17 W with laser central wavelength of 1064.6 nm. The minimum pulse duration is 75 ns at 488 kHz and the repetition rate is tunable from 300 to 807 kHz with the increase of the pump power. The maximum output power and highest pulse energy of the laser measured are 38.4 mW and 54.7 nJ respectively.