We propose a Q-switched Er-doped fiber laser (EDFL) with a threshold pumping power as low as 7.4 mW, and demonstrate using graphene polyvinyl alcohol (PVA) thin film as a passive saturable absorber (SA). The SA is fabricated from graphene flakes, which is synthesized by electrochemical exfoliation of graphite at room temperature in 1% sodium dodecyl sulfate aqueous solution. The flakes are mixed with PVA solution to produce a thin film, which is then sandwiched between two ferrules to form a SA and integrated in the EDFL ring cavity to generate a stable Q-switched pulse train. The pulse train operates at 1560 nm with a threshold pump power of 7.4 mW. At maximum 1480 nm pump power of 33.0 mW, the EDFL generates an optical pulse train with a repetition rate of 27.0 kHz and pulse width of 3.56 μs. The maximum pulse energy of 39.4 nJ is obtained at a pump power of 14.9 mW. This laser can be used as a simple and low-cost light source for metrology, environmental sensing, and biomedical diagnostics.