This　paper　studies　the　distributed　consensus　protocol　for　the　connected　vehicle　platoon　with　heterogeneous　time-varying　delays　and　switching　topologies.　A　third-order　dynamics　model　with　powertrain　inertial　lag　is　proposed　to　characterize　the　node　longitudinal　dynamics　of　vehicles　in　platoon.　A　novel　distributed　adaptive　consensus　protocol　considering　the　time-varying　delays　and　the　random　switched　inter-vehicular　communication　topologies　is　designed　to　stabilize　the　heterogeneous　vehicle　platoon　in　the　presence　of　external　disturbance.　The　delay-range-dependent　approach　is　used　to　deal　with　the　system　heterogeneous　time-varying　delays　by　considering　the　characteristics　of　the　heterogeneous　platoon.　Directed　graphs　are　adopted　to　describe　the　accessible　information　flow　among　vehicles.　The　necessary　and　sufficient　conditions　for　the　unified　closed-loop　vehicle　platoon　system　are　derived　by　using　matrix　analysis　and　Lyapunov-Krasovskii　approach.　Numerical　simulations　demonstrate　the　proposed　method　is　effective.