We experimentally observed three types of pulses generated in an erbium-doped fiber laser by incorporating a homemade graphene saturable absorber (GSA). The generated pulses from the laser oscillator include dual-wavelength dark pulses, fundamentally step-like pulses, and non-soliton second-harmonic pulses. These operation regimes are first reported by using graphene as the saturable absorber. Our results will further indicate that the GSA can function well for obtaining various ultrafast pulse phenomena, highlighting the practical potential of graphene in ultrafast photonics technologies.