We present superconducting nanowire single-photon detectors (SSPDs) on non-periodic dielectric multilayers, which enable us to design a variety of wavelength dependences of optical absorptance by optimizing the dielectric multilayer. By adopting a robust simulation to optimize the dielectric multilayer, we designed three types of SSPDs with target wavelengths of 500 nm, 800 nm, and telecom range respectively. We fabricated SSPDs based on the optimized designs for 500 and 800 nm, and evaluated the system detection efficiency at various wavelengths. The results obtained confirm that the designed SSPDs with non-periodic dielectric multilayers worked well. This versatile device structure can be effective for multidisciplinary applications in fields such as the life sciences and remote sensing that require high efficiency over a precise spectral range and strong signal rejection at other wavelengths.