The transporter MsbA is a kind of multidrug resistance ATP-binding cassette transporter that can transport lipid A, lipopolysaccharides, and some amphipathic drugs from the cytoplasmic to the periplasmic side of the inner membrane. In this work, we explored the allosteric pathway of MsbA from the inward- to outward-facing states during the substrate transport process with the adaptive anisotropic network model. The results suggest that the allosteric transitions proceed in a coupled way. The large-scale closing motions of the nucleotide-binding domains occur first, accompanied with a twisting motion at the same time, which becomes more obvious in middle and later stages, especially for the later. This twisting motion plays an important role for the rearrangement of transmembrane helices and the opening of transmembrane domains on the periplasmic side that mainly take place in middle and later stages respectively. The topological structure plays an important role in the motion correlations above. The conformational changes of nucleotide-binding domains are propagated to the transmembrane domains via the intracellular helices IH1 and IH2. Additionally, the movement of the transmembrane domains proceeds in a nonrigid body, and the two monomers move in a symmetrical way, which is consistent with the symmetrical structure of MsbA. These results are helpful for understanding the transport mechanism of the ATP-binding cassette exporters.