The　car-following　control　of　connected　and　automated　vehicles　(CAV)　is　studied　under　mixed　traffic　flow　with　regular　vehicles.　Considering　the　factors　of　velocity,　headway,　and　the　velocity　and　acceleration　difference　of　multiple　front　and　rear　vehicles,　this　paper　constructed　a　car-following　model　for　CAVs　by　using　the　molecular　dynamics　to　express　the　impacts　of　different　surrounding　vehicles　on　the　host　one.　The　car-following　process　of　CAVs　was　then　described　when　driving　in　the　traffic　mixed　with　CAVs　and　regular　human-driving　vehicles.　The　results　of　stability　analysis　show　that,　compared　with　the　full　speed　difference　model,　the　proposed　model　is　more　conducive　to　improving　the　stability　of　traffic　flow　due　to　the　consideration　of　multiple　front　and　rear　vehicles＇　information.　The　simulation　results　indicate　that,　compared　with　the　Cooperative　adaptive　cruise　control　(CACC)　model　provided　by　PATH　laboratory,　the　average　maximum　error　of　our　model　is　reduced　by　0.19　m/s,　the　average　error　is　reduced　by　26.79%,　and　the　fitting　accuracy　is　improved　by　0.91%.　Besides,　in　the　traffic　flow　mixed　with　CAV　and　RV,　with　the　increase　of　CAV　penetration,　the　average　velocity　of　the　platoon　and　volume　increase　gradually.　The　results　of　Hysteresis　loops　show　that　compared　with　the　Full　Velocity　Difference　(FVD)　model,　the　stability　of　traffic　flow　under　the　CAV　model　in　this　paper　is　better.　The　proposed　model　can　serve　as　an　effective　method　for　CAV　control　under　both　homogeneous　traffic　flow　or　heterogeneous　flow　mixed　with　CAVs　and　human-driving　vehicles.　Under　the　situation　that　it　is　difficult　to　carry　out　the　field　test　of　heterogeneous　flow　mixed　with　CAVs　and　human-driving　vehicles,　this　study　provides　a　theoretical　basis　and　model　support　for　vehicle　control　as　well　as　infrastructure　planning　and　design.　Copyright　©　2022　by　Science　Press.