We have studied a switchable hyperbolic metamaterial composed of a graphene–dielectric periodic structure. By tuning the chemical potential of all graphene sheets simultaneously, the isofrequency curve can switch between an ellipse and a hyperbola conveniently. In particular, a special hyperbolic isofrequency curve with its asymptote perpendicular to the interface is obtained and used to realize the zero reflection effect. Furthermore, a zero-reflection-based optical switch working in the terahe