Transition radiation (TR) induced by electron–matter interaction usually demands vast accelerating voltages, and the radiation angle cannot be controlled. Here we present a mechanism of direction controllable inverse transition radiation (DCITR) in a graphene-dielectric stack excited by low-velocity electrons. The revealed mechanism shows that the induced hyperbolic-like spatial dispersion and the superposition of the individual bulk graphene plasmons (GPs) modes make the fields, which are supposed to be confined on the surface, radiate in the stack along a special radiation angle normal to the Poynting vector. By adjusting the chemical potential of the graphene sheets, the radiation angle can be controlled. And owing to the excitation of bulk GPs, only hundreds of volts for the accelerating voltage are required and the field intensity is dramatically enhanced compared with that of the normal TR. Furthermore, the presented mechanism can also be applied to the hyperbolic stack based on semiconductors in the infrared region as well as noble metals in the visible and ultraviolet region. Accordingly, the presented mechanism of DCITR is of great significance in particle detection, radiation emission, and so on.