We consider a binary dipolar Bose-Einstein condensate confined in a rotating harmonic plus quartic potential trap. The ground-state vortex structures are numerically obtained as a function of the contact interactions and the dipole-dipole interaction in both slow and rapid rotation cases. The results show that the vortex configurations depend strongly on the strength of the contact interactions, the relative strength between dipolar and contact interactions, as well as on the orientation of the dipoles. A variety of exotic ground-state vortex structures, such as pentagonal and hexagon vortex lattice, square vortex lattice with a central vortex, annular vortex lines, and straight vortex lines, are observed by turning such controllable parameters. Our results deepen the understanding of effects of dipole-dipole interaction on the topological defects.