© 2018 American Physical Society. We demonstrate the development of a high-speed neutron-imaging system via a solid-state superconducting detector. Our developed system, a current-biased kinetic-inductance detector (CBKID), operates in a delay-line mode to identify the position of a local hot spot in terms of four different arrival time stamps at the ends of the delay lines. Our detector comprises X and Y superconducting Nb meander lines, which are fed by a weak dc current, and a B10 conversion layer, which converts a neutron into two charged particles. The high-energy light ions (He4 or Li7) in the B10(n,α)7Li reaction are able to create two hot spots simultaneously in the X and Y meanders. A pair of electromagnetic-wave pulses are generated at the hot spot and signals of different polarities start propagating on each of the X and Y meanders toward the ends. The position of the original hot spot is determined by the difference in arrival time of the two pulses at the two ends. To measure the arrival times of the pulse signals, we developed a set of analog signal discriminators from the preset threshold levels using a time-to-digital converter (TDC), which is able to record the timing of the propagated pulses with 1-ns resolution over a time frame of 4.2 s. We successfully reconstructed the neutron image of a test pattern with a spatial resolution of 22 μm and a detection rate tolerance of a few 10 MHz/cm2.