Individuals in depressed status respond abnormally to reward stimuli, but the neural processes involved remain unclear. Whether this neural response affects subsequent cognitive processing activities remains to be explored. In the current study, participants, screened as depressed status individuals and healthy individuals by Beck Depression Inventory and Hospital Anxiety Depression Scale, performed both a door task and a cognitive task. Specifically, in each trial, they selected one from two identical doors based on the expectations of rewards and punishments and received the rewarded or punished feedback, and then they performed a cognitive task in which they judged the correctness of a math equation. The neural responses of their choice in the door task were recorded. The results showed that when the two groups received punished feedback, their accuracy was significantly higher than they received rewarded feedback. Compared with the healthy group, the depressed status group spent more time completing cognitive tasks. Analysis of electroencephalography (EEG) data showed that the amplitude of RewP induced by rewarded feedback was larger than that induced by punished feedback, and the amplitude of RewP and fb-P3 induced by the depressed status group was smaller than that of the healthy group. The results of an order analysis showed that the main effects of group variable in fb-P3 and RewP appeared in the second half of the data, and the main effect of feedback type in RewP appeared in the first half of the data. The results showed that the neural response of individuals in depressed status to reward and punishment stimuli was weakened compared with healthy individuals and affected the subsequent cognitive processing to some extent. The effect of feedback appeared in the early stage and gradually decreased. The neural response of individuals in depressed status had a cumulative effect, and the differences appeared in the later stage. The results of this study support the emotional situation insensitive hypothesis, that is, individuals in depressed status are less sensitive to reward and punishment than healthy individuals.