© 2018, © 2018 Atomic Energy Society of Japan. All rights reserved. Even a zero-power reactor core containing highly enriched uranium has a weak neutron source inherent in uranium 235, and consequently, a neutron counter placed closely to the core without external neutron source registers a certain counting rate. The study of the counting is very important for zero-power reactor physics experiments with a high precision. In this experimental study, first, at a shutdown state of the UTR-Kinki reactor without start-up neutron source, a pulse height distribution of output signals from a neutron proportional counter was measured to confirm that these signals resulted from neutron detections. At several subcritical states of the UTR, then, the Feynman-α analysis was carried out to confirm that the neutrons detected by the counter must be fission neutrons multiplied by fission chain reactions. The correlation amplitude measured in the Feynman-α analysis was much higher than that measured in a previous drive by start-up source. Further, it was also confirmed that the subcriticality dependence of neutron counting rate followed the source multiplication formula. This feature indicated that the one-point model was very successful in the subcritical range including the shutdown state.