Abstract: Utilizing ultra-relativistic quantum molecular dynamics (UrQMD) model, the elliptic flow v_2 for proton and anti-protons as well as the v_2 difference between proton and anti-protons from ^197\rmAu+^197\rmAu collisions at center-of-mass energies \sqrts^_\rmNN=5\thicksim12 GeV are investigated. By comparing the results from the UrQMD model with and without potential interactions, the v_2 of protons and anti-protons and their difference as a function of the transverse momentum p_\rmt, incident energy \sqrts^_\rmNN, rapidity and centrality are analyzed. It is found that by including mean-field potentials, the transverse momentum, incident energy dependence of v_2 of protons and the v_2 difference in protons and anti-protons could be described well. And the v_2 difference is affected by the size of the windows (i.e. rapidity and centrality). These information are useful to understand the properties of nuclear matter at high density and thus exploring the structure of QCD (Quantum-ChromoDynamical) phase diagrams.