This　paper　proposes　a　predictive　constant　time　headway　spacing　strategy　(PCTHS)　for　the　heterogeneous　vehicle　platoon　control　problem.　This　strategy　uses　the　vehicle’s　own　speed　information　and　the　speed　information　of　the　leader　vehicle　associated　with　the　time　headway　to　improve　the　driving　safety　and　stability　of　the　vehicles　in　the　platoon.　Based　on　the　proposed　PCTHS,　a　corresponding　vehicle　following　control　protocol　is　designed.　The　proposed　control　protocol　has　a　flexible　general　frame　structure,　which　can　not　only　realize　the　consensus　of　the　position,　velocity　and　acceleration　of　heterogeneous　vehicles　in　the　platoon,　but　also　effectively　reduce　the　unreasonable　acceleration/deceleration　of　vehicles,　so　as　to　ensure　the　comfort　of　vehicles　during　driving.　Then,　the　stability　conditions　are　obtained　by　performing　state　linear　transformation　and　partial　stability　theory　analysis　on　the　vehicle　platoon　system.　Finally,　the　effectiveness　of　the　proposed　method　is　verified　by　the　simulation　of　a　third-order　heterogeneous　vehicle　platoon.　©　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.　2023.