Moiré nanosphere lithography (MNSL), which features the relative in-plane rotation between two layers of self-assembled monodisperse nanospheres as masks, provides a cost-effective approach for creating moiré patterns on generic substrates. In this work, we experimentally and numerically investigate a series of moiré metasurfaces by MNSL. Due to the variety of gradient plasmonic nanostructures in arrays, single moiré metasurfaces can support multiple localized surface plasmon (LSP) modes with a wide range of resonant wavelengths from ∼600 nm to ∼4200 nm. We analyze the origin of the LSP modes based on the optical spectra and near-field electromagnetic distributions. In addition, we fabricate and analyze the metasurfaces with high-density nanogap structures. These nanogap structures support plasmonic gap modes with significant field enhancements. With their tunable multiband optical responses from visible to near-infrared to mid-infrared regimes, these moiré metasurfaces are applicable for ultrabroadband absorbers, multiband surface-enhanced infrared and Raman spectroscopy, and broadband single-molecule spectroscopy.