Ultrafast fiber lasers with broad spectral coverage are in great demand for a variety of applications, such as spectroscopy, and biomedical diagnosis. Graphene is an ideal ultrawide-band saturable absorber. We report broadband (up to ~1000 nm) ultrafast pulse generation from three fiber lasers mode-locked by a single graphene saturable absorber device. The mode-locked pulses were based on Yb-, Er- and Tm:Ho-doped fiber lasers at the central wavelength of 1035, 1564, and 1908 nm, respectively. The maximum output energy is up to 16.2 nJ at 1908 nm. It is the first time that ultrafast fiber lasers covering 1, 1.5, and 2 μm spectral region are mode-locked with a single graphene device. Our results validate the intrinsic broadband operation property of graphene devices for all major fiber laser wavelengths from 1 to 2 μm.