Gait cycle variability during steady walking, described by the stride interval time series, has been used as a gait-stability-related measure. In particular, the positive persistency in the stride intervals with 1/f-like fluctuation and reduction of the persistency are the well-documented metrics that can characterize gait patterns of healthy young adults and elderly including patients with neurological diseases, respectively. Here, we examined effects of a dual task on gait cycle variability in healthy young adults, based on the mean and standard deviation statistics as well as the positive persistency of the stride intervals during steady walking on a treadmill. Specifically, three gait conditions were examined: control condition, non-cognitive task with holding a smartphone in front of the chest using their dominant hand and looking fixedly at a blank screen of the smartphone, and cognitive motor task with holding a smartphone as in the non-cognitive task and playing a puzzle game displayed on the smartphone by one-thumb operation. We showed that only the positive persistency, not the mean and standard deviation statistics, was affected by the cognitive and motor load of smartphone usage in the cognitive condition. More specifically, the positive persistency exhibited in the control and the non-cognitive conditions was significantly reduced in the cognitive condition. Our results suggest that the decrease in the positive persistency during the cognitive task, which might represent the deterioration of healthy gait pattern, is caused endogenously by the cognitive and motor load, not necessarily by the reduction of visual field as often hypothesized.