A Q-switched distributed Bragg reflector fiber laser using a graphene passive saturable absorber is proposed in a cavity consisting of a fiber Bragg grating and Faraday rotator mirror as end mirrors, together with a highly doped erbium-doped fiber as a gain source. The laser has a Q-switched threshold of about 28 mW and a tunable repetition rate of 10.4–18.0 kHz with varying pump power. The shortest pulse width obtained from the system is 3.7 μs, with a maximum pulse energy and peak power of 22.