Pleasure experience is an important part of normal healthy life and is essential for general and mental well-being. Many neuroimaging studies have investigated the underlying neural processing of verbal and visual modalities of reward. However, how the brain processes rewards in the olfactory modality is not fully understood. This study aimed to examine the neural basis of olfactory rewards in 25 healthy participants using functional magnetic resonance imaging (fMRI). We developed an Olfactory Incentive Delay (OLID) imaging task distinguishing between the anticipation and receipt of olfactory rewards and punishments. We found that the pallidum was activated during the anticipation of both olfactory rewards and punishments. The bilateral insula was activated independently from the odours' hedonic valence during the receipt phase. In addition, right caudate activation during the anticipation of unpleasant odours was correlated with self-reported anticipatory hedonic traits, whereas bilateral insular activation during the receipt of pleasant odours was correlated with self-reported consummatory hedonic traits. These findings suggest that activity in the insula and the caudate may be biomarkers of anhedonia. These findings also highlight a useful and valid paradigm to study the neural circuitry underlying reward processing in people with anhedonia.