The recognition of emotional facial expressions is critical for our social interactions. While some prior studies have shown that a high anxiety level is associated with more sensitive recognition of emotion, there are also reports supporting that anxiety did not affect or reduce the sensitivity to the recognition of facial emotions. To reconcile these results, here we investigated whether the effect of individual anxiety on the recognition of facial emotions is dependent on the emotion category and the race of the target faces. We found that, first, there was a significant positive correlation between the individual anxiety level and the recognition sensitivity for angry faces but not for sad or happy faces. Second, while the correlation was significant for both low- and high-intensity angry faces during the recognition of the observer's own-race faces, there was significant correlation only for low-intensity angry faces during the recognition of other-race faces. Collectively, our results suggest that the influence of anxiety on the recognition of facial emotions is flexible depending on the characteristics of the target face stimuli including emotion category and race.