We demonstrate a fiber-coupled fractal superconducting nanowire single-photon detector (SNSPD) system with minimum polarization dependence of detection efficiency. Its system detection efficiency (SDE) was maximized at the wavelength of 1540 nm, which was measured to be 91 ± 4%; furthermore, we observed the second local maximum of SDE at the wavelength of 520 nm, which was measured to be 61 ± 2%. This dual-band feature of SDE was due to the enhancement of the optical absorptance by two longitudinal resonance modes of the micro-cavity. By using high SDE with minimum polarization dependence in these two bands, we implemented a hybrid LIDAR for imaging the remote objects in free space and under water.