A fiber-based supercontinuum source, comprising a graphene mode-locked erbium fiber laser and a highly nonlinear photonic crystal fiber (PCF), is reported. The nonlinear fiber has zero-dispersion wavelength shifted towards 1500 nm specifically for pumping with compact femtosecond and sub-picosecond fiber lasers operating in this spectral area. A chirped pulse amplification system seeded by a graphene mode-locked laser, generating linearly polarized 850 fs pulses and a pulse energy of 20 nJ at a repetition rate of 50 MHz, was used as the pump source. A 6 cm long, soft-glass PCF sample enabled generation of a supercontinuum spanning over an octave from 1000 to over 2300 nm in a 20 dB dynamic range. The measured results are interpreted numerically, based on a solution to the nonlinear Schrödinger equation using the split-step Fourier method; assignment of the nonlinear processes taking part in the observed broadening is proposed. The developed model is then used to estimate supercontinuum performance in the presented fiber with improved experimental conditions.