Although trait anxiety has been associated with risk decision making, whether it is related to risk per se or to the feeling of the risk, as well as the underlying neurocognitive mechanisms, remains unclear. Using a decision-making task with a manipulation of frame (i.e., written description of options as a potential gain or loss) and functional magnetic resonance imaging, we investigated the neurocognitive relationship between trait anxiety and decision making. The classic framing effect was observed: participants chose the safe option when it was described as a potential gain, but they avoided the same option when it was described as a potential loss. Most importantly, trait anxiety was positively correlated with this behavioral bias. Trait anxiety was also positively correlated with amygdala-based "emotional" system activation and its coupling with the ventromedial prefrontal cortex (vmPFC) when decisions were consistent with the framing effect, but negatively correlated with the dorsal anterior cingulate cortex (dACC)-based "analytic" system activation and its connectivity to the vmPFC when decisions ran counter to the framing effect. Our findings suggest that trait anxiety is not associated with subjective risk preference but an evaluative bias of emotional information in decision making, underpinned by a hyperactive emotional system and a hypoactive analytic system in the brain.