The surface of W(110) exhibits a Dirac-cone-like state with d character within a spin-orbit-induced symmetry gap. As a function of the wave vector parallel to the surface, it shows a nearly massless energy dispersion and a pronounced spin polarization, which is antisymmetric with respect to the Brillouin zone center. In addition, the observed constant energy contours are strongly anisotropic for all energies. This discovery opens new pathways to the study of surface spin-density waves arising from a strong Fermi surface nesting as well as d-electron-based topological properties.