We demonstrate neutron detection using a solid state superconducting current biased kinetic inductance detector (CB-KID), which consists of a superconducting Nb meander line of 1 mu m width and 40 nm thickness. B-10-enriched neutron absorber layer of 150 nm thickness is placed on top of the CB-KID. Our neutron detectors are able to operate in a wide superconducting region in the bias current-temperature diagram. This is in sharp contrast with our preceding current-biased transition edge detector, which can operate only in a narrow range just below the superconducting critical temperature. The full width at half maximum of the signals remains of the order of a few tens of ns, which confirms the high speed operation of our detectors. (C) 2015 AIP Publishing LLC.