Single-layer graphene film is fabricated on the copper foil by using chemical vapor deposition method, and the corresponding Raman spectrum is measured. The graphene membrane is transferred to the facet of zirconium oxide of a fiber jumper. The mode-lock Er-doped fiber laser with few-layer graphene membrane as saturable absorber is experimentally studied, which has a ring structure and uses a 10% portion of a fiber coupler as the laser output. The laser generates a pulse train at a 7.69 MHz repetition rate, with a full width at half maximum of 58.8 ps. The corresponding time-bandwidth product is 1.98, indicating that the pulses are chirped. The peak wavelength and 3 dB bandwidth of the laser are 1560.1 nm and 0.27 nm respectively. Through changing the air gap between two the fiber ends, 4 nm wavelength tuning is observed.