Judgment of agency involves the comparison of motor intention and proprioceptive/visual feedback, in addition to a range of cognitive factors. However, few studies have experimentally examined the differences or correlations between delay detection ability and judgment of agency. Thus, the present study investigated the relationship between delay detection ability and agency judgment using the delay detection task and the agency attribution task. Fifty-eight participants performed the delay detection and agency attribution tasks, and the time windows of each measure were analyzed using logistic curve fitting. The results revealed that the time window of judgment of agency was significantly longer than that of delay detection, and there was a slight correlation between the time windows in each task. The results supported a two-step model of agency, suggesting that judgment of agency involved not only comparison of multisensory information but also several cognitive factors. The study firstly revealed the model in psychophysical experiments.