Vehicle　to　anything　(V2X),　especially　vehicle-to-vehicle　(V2V)　technology,　is　regarded　as　a　promising　technology　to　improve　traffic　efficiency　and　safety.　Under　V2V　environment,　drivers　can　communicate　with　each　other,　and　obtain　the　real-time　information　of　followers,　besides　of　that　from　the　preceding　vehicle.　According　to　the　condition　of　sending　a　request　of　cooperative　driving　to　the　preceding　vehicle,　drivers　are　categorized　into　three　sensitivity　types,　i.e.　aggressive,　normal　and　conservative.　The　mechanism　of　the　driver＇s　reaction　to　the　backward　request　is　also　presented.　Then,　a　safety　rule-based　cellular　automaton　(CA)　model　is　developed,　which　involves　bi-directional　vehicular　information.　Finally,　through　numerical　experiments,　the　influences　of　cooperative　driving　by　V2V　on　traffic　efficiency　and　safety　are　analyzed　and　concluded　as　follows.　1)　The　cooperative　driving　is　conducive　to　improving　the　efficiency　of　vehicles　to　achieve　their　desired　states　when　the　speed　constraint　(of　head　vehicle)　is　serious;　2)　The　higher　average　danger　coefficient　is　produced　in　the　more　congested　vehicular　fleet;　3)　With　regard　to　homogeneous　vehicle　fleets,　more　aggressive　driving　behaviors　with　V2V　communication　results　in　the　lower　safety　performance,　but　can　increase　the　traffic　flux　at　synchronized　flow　and　congested　state;　4)　As　for　heterogeneous　vehicle　fleets,　the　stimulation　type,　the　sensitivity　type,　and　the　orders　of　sensitivity　types　all　have　an　important　effect　in　the　safety　performance.　©　2018,　©　2018　Hong　Kong　Society　for　Transportation　Studies　Limited.