While viewing faces, humans often demonstrate a natural gaze bias towards the left visual field, that is, the right side of the viewee's face is often inspected first and for longer periods. Previous studies have suggested that this gaze asymmetry is a part of the gaze pattern associated with face exploration, but its relation with perceptual processing of facial cues is unclear. In this study we recorded participants' saccadic eye movements while exploring face images under different task instructions (free viewing, judging familiarity and judging facial expression). We observed a consistent left gaze bias in face viewing irrespective of task demands. The probability of the first fixation and the proportion of overall fixations directed at the left hemiface were indistinguishable across different task instructions or across different facial expressions. It seems that the left gaze bias is an automatic reflection of hemispheric lateralisation in face processing, and is not necessarily correlated with the perceptual processing of a specific type of facial information.