High trait anxiety is a risk factor for the development of anxiety disorders. Like the disorders themselves high trait anxiety has marked phenotypic variation at the level of symptomatology and neural circuits, suggesting that there may be different symptoms and distinct neural circuits associated with risk for these disorders. To address these issues, it is essential to develop reliable animal models of trait anxiety in a non-human primate whose brain bears structural and functional similarity to humans. The present study investigated individual variation in responsivity to fearful and anxiety provoking stimuli in the common marmoset monkey. Seven out of 27 animals failed to display discriminative, conditioned cardiovascular and behavioral responses on an auditory fear discrimination task, similar to that seen in high anxious humans and rodents. Their heightened emotionality to a rubber snake was consistent with the hypothesis that they were high in trait-like anxiety. Evidence for phenotypic variation in the high anxiety group was provided by the finding that discrimination failure was predicted early in conditioning by either hyper-vigilant scanning to the cues or a reduction in blood pressure to the context, i.e., test apparatus. Given that high trait anxiety in humans can be associated with altered prefrontal cognitive functioning and previously we implicated the marmoset anterior orbitofrontal (antOFC) and ventrolateral prefrontal cortex (vlPFC) in negative emotion regulation, we also tested the marmosets on two tests of cognitive flexibility differentially dependent on these two regions. While the high anxious group did not differ overall in their perseverative performance, the two distinct phenotypes were differentially correlated with reduced perseverative responding on the OFC- and vlPFC-dependent flexibility tests. Together, this study provides a new model of trait anxiety in marmosets amenable to analysis of phenotypic variation and neural circuitry.