Impulsivity, which is linked to a wide range of psychiatric disorders, is often characterized by a preference for immediate but smaller rewards over delayed but larger rewards. However, debate exists on the relationship between anxiety and impulsivity. Here we use event-related potential (ERP) components as biomarkers in the temporal discounting task to examine the effect of anxiety on inter-temporal decision-making. Our behavioral results indicated that the high trait anxiety (HTA) group made significantly more immediate choices than the low trait anxiety (LTA) group. Compared with the LTA group, shorter response time was associated with immediate rewards in the HTA group. Furthermore, previous studies have demonstrated three ERP components that are associated with impulsivity and/or delay discounting. First, the N1 is an early sensory component involved in selective attention and attention processing for goal-directed actions. Second, the reward positivity (RewP) reflects reward-related dopaminergic activity and encodes reward values. Third, the P3 is regarded as a measure of motivational significance in the decision-making literature. Accordingly, this study found in the immediate-option-evoked ERPs that the HTA group had a larger N1 than the LTA group did. For the delayed-option-evoked ERPs, the HTA group had larger N1 and RewP for the immediate choice than the LTA group did, while the LTA group had a larger P3 for the delayed choice than the HTA group did. These results support the notion that anxiety individuals are impulsive decision-makers in the Delay Discounting Task.