Head movements can provide a significant amount of information in communication. This study investigated the social capabilities of a robot’s head interaction, including the direction, movement, and timing of the movement. Using a newly designed robot, which has a minimal head movement mechanism in the three axes of x (pitch), y (roll), and z (yaw), we explored the participants’ perception of the robot’s head movements (i.e., nodding, shaking, and tilting) and movement timing (i.e., head movement prior to utterance and head movement simultaneous with utterance). The results revealed that head movements of the robot increased participants’ perceptions of likeability, anthropomorphism, animacy, and perceived intelligence of the robot compared with the non-movement condition. When the robot performed head movement prior to utterance, the rating of perceived naturalness was higher compared with that when the robot’s head movement occurred simultaneously with utterance. The findings imply that by implementing the features of head movements and movement timings, even simple robots that lack humanoid features can achieve better social interactions with humans.