Despite various studies examining intertemporal choice with hypothetical rewards due to problematic real reward delivery, there remains no substantial evidence on the effect of the incentives on the decision confidence and cognitive process in intertemporal choice and no comprehensive exploration on the loss domain. Hence, this study conducts an eye-tracking experiment to examine the effect of incentive approach and measure participants' decision confidence using a between-subject design in both gain and loss domains. Results replicated previous findings which show incentives do not affect intertemporal choice in the gain domain. In contrast, in the loss domain, participants in the incentivized group were more likely to choose the larger-later options than those in the non-incentivized group. Furthermore, the decision confidence and the mean fixation duration differed between the incentivized and non-incentivized groups in both gain and loss domains. These findings allow for a better understanding of the effect of incentives on intertemporal choice and provide valuable information for the design of incentives in future intertemporal experiments.