Theoretical accounts have linked anxiety to intolerance of ambiguity. However, this relationship has not been well operationalized empirically. Here, we used computational and neuro-imaging methods to characterize anxiety-related differences in aversive decision-making under ambiguity and associated patterns of cortical activity. Adult human participants chose between two urns on each trial. The ratio of tokens (Os and Xs) in each urn determined probability of electrical stimulation receipt. A number above each urn indicated the magnitude of stimulation that would be received if a shock was delivered. On ambiguous trials, one of the two urns had tokens occluded. By varying the number of tokens occluded, we manipulated the extent of missing information. At higher levels of missing information, there is greater second order uncertainty, i.e., more uncertainty as to the probability of pulling a given type of token from the urn. Adult human participants demonstrated avoidance of ambiguous options which increased with level of missing information. Extent of information-level dependent ambiguity aversion was significantly positively correlated with trait anxiety. Activity in both the dorsal anterior cingulate cortex and inferior frontal sulcus during the decision-making period increased as a function of missing information. Greater engagement of these regions, on high missing information trials, was observed when participants went on to select the ambiguous option; this was especially apparent in high trait anxious individuals. These findings are consistent with individuals vulnerable to anxiety requiring greater activation of frontal regions supporting rational decision-making to overcome a predisposition to engage in ambiguity avoidance at high levels of missing information.