We have studied the tunable properties of a hyperbolic metamaterial (HMM) composed of alternative dielectric layers and graphene sheets, and proposed a highly directional emission device working in the terahertz region. By changing the chemical potential , the equifrequency contour (EFC) of the HMM is easily switched between elliptical and hyperbolic types. Especially, when a dipole source is placed inside the structure, highly directional emission is realized provided that the EFC is a flat ellipse. Interestingly, such highly directional emission can be achieved for any frequency within a broad frequency range by tuning the chemical potential . The divergence angle of such a directional beam is lower than 12°. Additionally, the influences of structural parameters ( and d) on the working bandwidth are also studied. These results have potential in many fields such as light coupling and spontaneous radiation antennas.