Optical beams carrying orbital angular momentum (OAM) play an important role in micro-/nanoparticle manipulation and information multiplexing in optical communications. Conventional OAM generation setups require bulky optical elements and are unsuitable for on-chip integration. OAM generators based on metasurfaces can achieve ultracompact designs. However, they generally have limited working bandwidth and require complex designs and multistep time-consuming fabrication processes. In comparison, graphene metalenses based on the diffraction principle have simple designs and can be fabricated by laser nanoprinting in a single step. Here, we demonstrate that a single ultrathin (200 nm) graphene OAM metalens can integrate OAM generation and high-resolution focusing functions in a broad bandwidth, covering the entire visible wavelength region. Broadband graphene OAM metalenses with flexibly controlled topological charges are analytically designed using the detour phase method considering the dispersionless feature of the graphene material and fabricated using ultrafast laser nanoprinting. The experimental results agree well with the theoretical predictions, which demonstrate the accuracy of the design method. The broadband graphene OAM metalenses can find broad applications in miniaturized and integrated photonic devices enabled by OAM beams.