Anxiety can either impair or enhance performance depending on the context. Increased sensitivity to threat seems to be an important feature of sensory processing in anxiety since anxious individuals tend to be more attentive to threatening visual stimuli. Evidence of anxiety effects in olfaction is rare; though alterations of olfactory performance in psychiatric patients and some effects of trait and state anxiety on olfactory performance have been reported. Our main objective was thus to investigate whether olfactory processing speed varies as a function of trait anxiety levels. We additionally investigated a possible preferential bias for unpleasant odors in highly anxious participants. Thirty-eight healthy adults participated in a simple odor detection task, where response times (RTs) and anxiety levels were measured. We compared RTs to a pleasant and an unpleasant food odor between high- and low-trait anxiety participants. We found that high-trait anxiety participants detected both odors faster than low-trait anxiety participants, independently of odor pleasantness. Moreover, trait anxiety levels significantly correlated with reaction times to both odors, indicating that trait anxiety but not odor pleasantness influences olfactory detection speed. These findings provide new insights into olfactory processing in healthy adults showing how various levels of trait anxiety affect the olfactory modality.