Previous research suggested that individuals with high trait anxiety have difficulties disengaging their attention from threatening cues, whereas those with low trait anxiety have no such attentional bias. However, according to some cognitive models of threat-related attention, low anxious people should show the same pattern as high anxious people when the threat value is large enough. To test this hypothesis, extremely threatening pictures were used as predictive location cues in a cue-target task. Neutral pictures were included as controls. 15 High Anxious participants and 17 Low Anxious participants were selected from 213 volunteers who all were police veterans. Analysis showed that threat cues produced greater facilitation effects than neutral cues, but this was not modulated by anxiety. This suggests that both high and low anxious individuals may have difficulties disengaging their attention from threat-cued locations when the threat value is large enough.