Intertemporal decision-making is the choice between an immediate smaller reward (SS) and a delayed larger reward (LL). Intertemporal decision-making depends on the interaction of the cognitive and emotional systems, and the latter is particularly vital. According to the Appraisal Tendency Frame (ATF) theory, anger influences intertemporal decision-making by increasing an individual's sense of certainty and control. This study examined whether anger affects intertemporal decision-making in individuals with internet addiction (IA) in this manner and investigated its neural mechanisms. Nineteen individuals with IA and 20 healthy controls were recruited. All subjects performed the Monetary choice task under anger and neutral emotions while functional near-infrared spectroscopy (fNIRS) equipment simultaneously recorded the hemodynamics in the prefrontal cortex (PFC). Individuals with IA showed a more considerable delay discount and lower brain activations in the orbitofrontal cortex (OFC) and left dorsolateral prefrontal cortex (L-dlPFC) compared to HC. Moreover, individuals with IA made more LL choices in the angry condition than in the neutral emotion, yet there was no difference in HC. The brain activation in L-dlPFC of individuals with IA tends to increase in the angry condition compared to the neutral condition. These findings revealed that impairment of intertemporal decision-making in individuals with individuals with IA might be related to the dysfunction of OFC and L-dlPFC. Our work also provided initial footing for the applicability of the appraisal tendency frame theory to individuals with IA, and L-dlPFC might play a role in the effects of anger on intertemporal decision-making.