Non-line-of-sight (NLOS) imaging can visualize a remote object out of the direct line of sight and can potentially be used in endoscopy, unmanned vehicles, and robotic vision. In an NLOS imaging system, multiple diffusive reflections of light usually induce large optical attenuation, and therefore, a sensitive and efficient photodetector, or, their array, is required. Limited by the spectral sensitivity of the light sensors, up to now, most of the NLOS imaging experiments are performed in the visible bands, and a few at the near-infrared, 1550 nm. Here, to break this spectral limitation, we demonstrate a proof-of-principle NLOS imaging system using a fractal superconducting nanowire single-photon detector, which exhibits intrinsic single-photon sensitivity over an ultra-broad spectral range. We showcase NLOS imaging at 1560- and 1997-nm two wavelengths, both technologically important for specific applications. We develop a de-noising algorithm and combine it with the light-cone-transform algorithm to reconstruct the shape of the hidden objects with significantly enhanced signal-to-noise ratios. We believe that the joint advancement of the hardware and the algorithm presented in this paper could further expand the application spaces of the NLOS imaging systems.