The origin of chemically peculiar stars and nonzero eccentricity in evolved close binaries have been long-standing problems in binary stellar evolution. Answers to these questions may trace back to an intense mass transfer during the asymptotic-giant-branch (AGB) binary phase. We use AstroBEAR to solve the 3D radiation hydrodynamic equations and calculate the mass transfer rate in AGB binaries that undergo the wind-Roche-lobe overflow or Bondi-Hoyle-Lyttleton (BHL) accretion. One of the goals of this work is to illustrate the transition from the wind- Roche-lobe overflow to BHL accretion. Both circumbinary disks and spiral structure outflows can appear in the simulations. As a result of enhanced mass transfer and angular momentum transfer, some AGB binaries may undergo orbit shrinkage, and some will expand. The high mass transfer efficiency is closely related to the presence of the circumbinary disks.