We investigated the processing of threat-related, positive, and neutral words in parafoveal and in foveal vision as a function of individual differences in trait anxiety. In a lexical-decision task, word primes were presented for 150 ms either parafoveally (2.2° away from fixation; Experiment 1) or foveally (at fixation; Experiment 3) followed by a probe word; or a foveal probe word was presented alone (with no prime; Experiment 2). Results showed that parafoveal prime threat words facilitated responses to probe threat words for high-anxiety individuals, in comparison with neutral and positive words, and relative to low-anxiety individuals. In contrast, when the words were presented foveally, there were no differences in resting activation level (i.e., accessibility to single word meanings) or firing thresholds (i.e., foveal priming) as a function of emotional content and anxiety. This reveals a covert attention bias towards threat stimuli in anxiety.