Light beams carrying orbital angular momentum (OAM) have inspired various advanced applications, and such abundant practical applications in turn demand complex generation and manipulation of optical vortices. Here, we propose a multifocal graphene vortex generator, which can produce broadband angular momentum cascade containing continuous integer non-diffracting vortex modes. Our device naturally embodies a continuous spiral slit vortex generator and a zone plate, which enables the generation of high-quality continuous vortex modes with deep depths of foci. Meanwhile, the generated vortex modes can be simultaneously tuned through incident wavelength and position of the focal plane. The elegant structure of the device largely improves the design efficiency and can be fabricated by laser nanofabrication in a single step. Moreover, the outstanding property of graphene may enable new possibilities in enormous practical applications, even in some harsh environments, such as aerospace.