We study the band structure modulation and spin-Hall effect of an irradiated two-dimensional heavy-hole system with k3-Rashba spin-orbit coupling. We find that the band structure becomes anisotropic under the illumination by the light. Most remarkably, in the presence of linearly polarized light a pair of additional spin-degeneracy points, apart from the Γ point, emerge in the energy dispersion. The locations of these points are solely determined by the amplitude of the incident light. If this degeneracy occurs around the Fermi level, the spin-Hall conductivity exhibits a resonance. Away from the degeneracy points, the light rotates the average spin polarization. The possible effects of k3-Dresselhaus spin-orbit coupling are also discussed.