The study on magnetoelectric effect in hexagonal perovskite structure HoMnO3 has become a very important aspect in the research of multiferroic materials. In this paper, using the first principles based on the generalized gradient approximation of density functional theory and considering the noncollinear magnetic structure calculation, the effects of the interation between on-site Coulomb of d electron and spin-orbit coupling on the electronic density of states and energy band structure of HoMnO3 are calculated and investigated. The calculations show that due to the on-site Coulomb interaction, the strong hybridization of Ho 5d with O(3, 4) 2p and Mn 3d with O(1, 2) 2p orbits are considered as the origin of driving force for the ferroelectric distortion. At the same time, the distributions of the energy gap and energy band provide a theoretical support for the explanation of strong optical absorption peak in experiment. In addition, the spin-orbit coupling makes the orbital hybridization of Mn 3d with O(3, 4) 2p within the ab plane strengthened, and the partial energy degeneracy in the ab plane is eliminated. The HoMnO3 is shown to possess the insulator characteristics of typical indirect energy gap.