An abnormal increase in the SDE was observed for superconducting nanowire single-photon detectors (SNSPDs) when the bias current (I(b)) was close to the switching current (I(sw)). By introducing the time-correlated single-photon counting technique, we investigated the temporal histogram of the detection counts of an SNSPD under illumination. The temporal information helps us to distinguish photon counts from dark counts in the time domain. In this manner, the dark count rate (DCR) under illumination and the accurate SDE can be determined. The DCR under moderate illumination may be significantly larger than the conventional DCR measured without illumination under a high I(b), which causes the abnormal increase in the SDE. The increased DCR may be explained by the suppression of I(sw) under illumination.