Patterned arrays of graphene nanostructures, also referred as graphene metasurfaces, have proven to be capable of efficiently coupling with incident light by surface plasmon resonances. In this work, a new type of graphene metasurfaces with moiré patterns using cost-effective and scalable moiré nanosphere lithography (MNSL) is demonstrated. A large gradient in feature size (i.e., from sub-200 nm to 1.1 μm) of the graphene nanostructures exists in single metasurfaces. The in-plane quasi-periodic arrangement of the graphene nanostructures can be easily tuned to form a variety of moiré patterns. The experimental measurement and numerical simulations show that the graphene moiré metasurfaces support tunable and multiband optical responses due the size and shape dependences of surface plasmon resonance modes of graphene nanostructures. It is also demonstrated that the multiband optical responses of graphene moiré metasurfaces can be tuned from mid-infrared (MIR) to terahertz (THz) regimes by choosing polystyrene spheres of different sizes for MNSL. These findings provide a cost-effective and scalable strategy to achieve ultrathin functional devices, including multiband light modulators, broadband biosensors, and multiband photodetectors, which feature tunable and multiband responses in wide range of wavelengths from MIR to THz.