In this research, we study analytically the double-chain model for deoxyribonucleic acid (DNA). The Φ 6-model expansion method is used to extract the traveling wave solutions to double chain model of DNA that plays an important role in biology. The solutions obtained by this mechanism can be divided into solitary, singular, kink, single wave, combine behavior as well as a hyperbolic, plane wave, trigonometric, and the families of Jacobi solutions for elliptic functions with arbitrary parameters. The results show that the system theoretically has extremely rich exact wave structures of biological relevance.