High-efficiency superconducting nanowire single-photon detectors (SNSPDs), which have numerous applications in quantum information systems, function by using the optical cavity and the ultrasensitive photon response of their ultra-thin superconducting nanowires. However, the wideband response of superconducting nanowires is limited due to the resonance of the traditional optical cavity. Here, we report on a supercontinuum SNSPD that can efficiently detect single photons over an ultra-broad spectral range from visible to mid-infrared light. Our detection approach relies on using multiple cavities with well-separated absorbed resonances formed by fabricating multilayer superconducting nanowires on metallic mirrors with silica acting as spacer layers. Thus, we are able to extend the absorption spectral bandwidth while maintaining considerable efficiency, as opposed to a conventional single-layer SNSPD. Our calculations show that the proposed supercontinuum SNSPD exhibits an extended absorption bandwidth with increased nanowire layers. Its absorption efficiency is greater than 70% over the entire range from 400 to 2500 nm (or 400 to 3000 nm), when using two-layer (or three-layer) nanowires. As a proof of principle, the SNSPD with bilayer nanowires is fabricated based on the proposed detector architecture with simplified geometrical parameters. The detector achieves broadband detection efficiency over 60% from 950 to 1650 nm. This type of detector may replace multiple narrow band detectors in a system and find uses in the emerging and rapidly advancing field of atomic and molecular broadband spectroscopy.