The facial expressions of humanoid robots play a crucial role in human–computer information interactions. However, there is a lack of quantitative evaluation methods for the anthropomorphism of robot facial expressions. In this study, we designed and manufactured a humanoid robot head that was capable of successfully realizing six basic facial expressions. The driving force behind the mechanism was efficiently transmitted to the silicone skin through a rigid linkage drive and snap button connection, which improves both the driving efficiency and the lifespan of the silicone skin. We used human facial expressions as a basis for simulating and acquiring the movement parameters. Subsequently, we designed a control system for the humanoid robot head in order to achieve these facial expressions. Moreover, we used a flexible vertical graphene sensor to measure strain on both the human face and the silicone skin of the humanoid robot head. We then proposed a method to evaluate the anthropomorphic degree of the robot’s facial expressions by using the difference rate of strain. The feasibility of this method was confirmed through experiments in facial expression recognition. The evaluation results indicated a high degree of anthropomorphism for the six basic facial expressions which were achieved by the humanoid robot head. Moreover, this study also investigates factors affecting the reproduction of expressions. Finally, the impulse was calculated based on the strain curves of the energy consumption of the humanoid robot head to complete different facial expressions. This offers a reference for fellow researchers when designing humanoid robot heads, based on energy consumption ratios. To conclude, this paper offers data references for optimizing the mechanisms and selecting the drive components of the humanoid robot head. This was realized by considering the anthropomorphic degree and energy consumption of each part. Additionally, a new method for evaluating robot facial expressions is proposed.