We have developed a single-photon detector that uses an InGaAs avalanche photodiode (APD) operating in sub-Geiger mode. Sub-Geiger mode operation is a technique in which an APD is operated at a bias voltage that is lower than the breakdown voltage. This mode considerably reduces afterpulse probability, and single photons that arrive randomly can be detected. In the present study, we reduced the dark count rate of the sub-Geiger mode single-photon detector by using a low-dark-current InGaAs APD. Consequently, we obtained a dark count rate (DCR) of 5.6 counts per second (cps) with single-photon detection efficiency (SPDE) of 0.2%. Our single-photon detector is comparable in DCR to that of superconducting nanowire single-photon detectors.