Due to its unique electronic property and the Pauli blocking principle, atomic layer graphene possesses wavelength-independent ultrafast saturable absorption, which can be exploited for the ultrafast photonics application. Through chemical functionalization, a graphene-polymer nanocomposite membrane was fabricated and first used to mode lock a fiber laser. Stable mode locked solitons with 3 nJ pulse energy, 700 fs pulse width at the 1590 nm wavelength have been directly generated from the laser. We show that graphene-polymer nanocomposites could be an attractive saturable absorber for high power fiber laser mode locking.