This　article　studies　the　problem　of　cooperative　control　of　heterogeneous　vehicles　in　a　platoon.　First,　a　novel　predictive　spacing　strategy　(PSS)　is　proposed　for　vehicles　that　are　described　by　a　third-order　heterogeneous　dynamics　model.　The　PSS　utilizes　the　current　velocity　information　of　each　vehicle　to　predict　its　travel　distance　forward,　thereby　enhancing　the　control　performance　of　the　vehicle　platoon.　Second,　the　vehicle　platooning　problem　is　equivalently　transformed　into　a　leader-following　consensus　(LFC)　for　multi-vehicle　system　by　introducing　new　variables,　and　in　this　way　a　distributed　linear　control　protocol　with　a　generalized　structure　is　proposed.　Then,　we　cleverly　employ　a　linear　transformation　based　on　a　directed　spanning　tree　(DST)　to　further　convert　the　consensus　problem　into　an　asymptotic　stability　problem　with　partial　variables　of　the　equivalent　system.　On　this　basis,　the　conditions　for　achieving　platoon　control　in　the　multi-vehicle　system　are　derived　in　conjunction　with　the　partial　stability　theory,　and　the　conditions　for　the　system　to　satisfy　string　stability　are　further　deduced.　In　addition,　a　method　for　solving　the　gain　matrix　in　the　control　protocol　is　elaborated.　Finally,　the　effectiveness　of　the　proposed　PSS　and　the　designed　protocol　is　verified　by　numerical　simulation.