By the methods of Jordan–Wigner transformation and Bogolyubov transformation, in this paper, we diagonalized the Hamiltonian in one-dimensional Heisenberg spin chain model with Dzyaloshinskii–Moriya interactions and three-body interactions, and further analyze the effect of the Dzyaloshinskii–Moriya interaction and different three-body interactions on the Bogolyubov transformation and the energy spectrum of quantum spin chains. The results shows that only the energy spectrum but not the coefficients of the Bogolyubov transformation depends on DM interaction and one type of three-site exchange interaction. Another kind of three-body interaction not only can move the criticality region, but also can generate a new critical point.