The ground electronic state and the reasonable dissociation limit of HNO molecule are determined based on the group theory and the atomic and molecular reaction statics. The energy, the equilibrium geometry and the harmonic frequency of the ground electronic state of HNO are calculated using the density functional theory B3LYP method in combination with the 6-311G ** basis set. The computational results show that the ground state of HNO molecule has CS symmetry, its ground electronic state is X1A', and the equilibrium parameters of the structure are RHN=0.1065nm, RNO=0.1200 nm,HNO=108.60, dissociation energy De=15.379 eV, bending vibrational frequency 1=1575.6351 cm-1, symmetric stretch frequency 2=1673.2890 cm-1, and asymmetric stretch frequency 3=2837.7856 cm-1. Then the analytic potential energy function of HNO molecule is derived by the many-body expansion theory. The potential curves correctly describe the configurations and the dissociation energy for the HNO molecule.