Most existing special beams(focused beams, Airy beams, etc.) metasurfaces usually use metallic materials for a single wavefront modulation by changing the dimensions of the cell structure, the angle of rotation, etc. There are fewer researches on metasurfaces for special beams with dynamically tunable wavefronts. Therefore, breaking the barrier of traditional structures, special beam metasurfaces which utilize Fermi energy levels of graphene to dynamically modulate the wavefront are constructed.Stronger freedom in dynamically modulating the wavefront can be realized in order to achieve more and more complex phase requirements. Focusing metasurfaces with tunable wavefront and tunable Airy beam metasurfaces are designed, different phase distributions are obtained by tuning the Fermi energy levels of graphene. Utilizing the dynamic wavefront, the spatial position of the focal point, the switching of the focusing switch with the number of focal points, and the parameters affecting the Airy beam can be regulated. The proposed dynamic tunable wavefront special beam metasurfaces are helpful for terahertz applications in high-resolution imaging, focus-tunable planar lenses, optical micromanipulation, laser micromachining, and optical bullet molding.