As a continuum model of DNA, a thin elastic rod subjected to interfacial interactions is used to investigate the equilibrium configuration of DNA in salt solution. In this paper the anisotropic bending elasticity models are established to characterize the change of the interfacial traction and the elastic modulus. The influences of the ionic concentration and anisotropic bending elasticity on the equilibrium configuration of DNA are discussed. The results show that the condensation of DNA is mainly determined by the interfacial tractions and the bending elasticity. With the change of the elasticity, the DNA segments will undergo a series of alteration from the original configuration to the condensed configuration, and the spiral-shape appearing in the condensed configuration of DNA shows a fairly well agreement with experimental observation.