A passively mode-locked erbium-doped fiber soliton laser based on graphene saturable absorber is reported. At a pump power of 370.4 mW, the pulse width is about 1.32 ps and the pulse repetition rate is 3.16 MHz with average output power of 1.07 mW, which corresponds to single pulse energy of 0.338 nJ. Moreover, the central wavelength can be tuned between 1556.72 nm and 1558.76 nm. The simulation based on Ginzburg-Landau equation is consistent with the experimental results.