We investigated whether categorical perception and dimensional perception can co-occur while decoding emotional facial expressions. In Experiment 1, facial continua with endpoints consisting of four basic emotions (i.e., happiness-fear and anger-disgust) were created by a morphing technique. Participants rated each facial stimulus using a categorical strategy and a dimensional strategy. The results show that the happiness-fear continuum was divided into two clusters based on valence, even when using the dimensional strategy. Moreover, the faces were arrayed in order of the physical changes within each cluster. In Experiment 2, we found a category boundary within other continua (i.e., surprise-sadness and excitement-disgust) with regard to the arousal and valence dimensions. These findings indicate that categorical perception and dimensional perception co-occurred when emotional facial expressions were rated using a dimensional strategy, suggesting a hybrid theory of categorical and dimensional accounts.