Achieving ultra-broadband and completely modulated absorption enhancement of monolayer graphene in near-infrared region is practically important to design graphene-based optoelectronic devices, however, which remains a challenge. In this work, by spectrally designing multiple magnetic plasmon resonance modes in metamaterials to be adjacent to each other, near-infrared light absorption in monolayer graphene is greatly improved to have an averaged absorption efficiency exceeding 50% in a very broad absorption bandwidth of about 800 nm. Moreover, by exerting an external bias voltage on graphene to change Fermi energy of graphene, the ultra-broadband absorption enhancement of monolayer graphene exhibits an excellent tunability, which has a nearly 100% modulation depth and an electrical switching property. This work is promising for applications in near-infrared photodetectors, amplitude modulators of electromagnetic waves, etc.