Owing　to　the　proposal　of　new　infrastructure　construction　strategies　and　the　development　of　autonomous　driving　and　connected　network　communication　technologies,　mixed-traffic　flows,　which　consist　of　connected　and　automated　vehicles(CAV),　autonomous　vehicles(AV),　and　regular　vehicles(RV),　are　expected　to　exist　for　a　long　time.　This　paper　proposes　a　mixed-flow　following　model　for　three　types　of　vehicles-connected　and　automated　vehicles,　autonomous　vehicles,　and　regular　vehicles-considering　the　headway　of　multiple　front　and　rear　vehicles,　the　velocity　and　acceleration　differences　between　multiple　front　vehicles　and　the　host　vehicle,　and　the　relative　distance　from　the　host　vehicle.　In　addition,　numerical　simulations　involving　typical　scenarios　were　conducted.　Brake　and　start　the　process　of　three　types　of　mixed-flow　numerical　simulation　results　indicate　that　the　model　is　feasible　under　several　typical　scenarios.　The　acceleration　and　velocity　of　the　vehicle　changed　more　gently.　Results　of　the　numerical　simulations　with　different　CAV　ratios　indicate　that,　the　higher　the　CAV　ratio　of　the　fleet,　the　shorter　is　the　time　required　for　the　overall　fleet　to　recover　to　a　stable　state　and　the　smaller　is　the　fluctuation　range.　The　numerical　simulation　results　for　the　CAV　homogeneous　flow　indicate　that　the　unstable　region　of　the　MFRHVAD　model　is　reduced　by　33.　8%　and　the　velocity　fluctuation　range　of　the　fleet　controlled　by　the　MFRHVAD　model　is　reduced　by　14%,　as　compared　with　those　when　using　the　MHVAD　model.　Furthermore,　the　numerical　simulation　results　for　mixed　CAV　and　AV　flows　indicate　that　the　acceleration　of　the　fleet　controlled　by　the　MFRHVAD　model　enters　a　relatively　stable　state　5.　5　s　before　that　when　using　the　PATH　laboratory　model.　This　model　can　be　utilized　for　the　queue　control　of　homogeneous　and　mixed-traffic　flows.　In　situations　where　it　is　difficult　to　perform　actual　vehicle　experiments　with　mixed-traffic　flows,　this　model　can　be　applied　for　simulating　the　car-following　behavior;　hence,　it　can　be　helpful　for　road　traffic　management　and　developing　infrastructure　layouts　for　mixed-traffic　flows.　©　2021,　Editorial　Department　of　China　Journal　of　Highway　and　Transport.　All　right　reserved.