Vehicular　Ad　hoc　Networks　(VANETs)　have　higher　requirements　of　continuous　Location-Based　Services　(LBSs).　However,　the　untrusted　server　could　reveal　the　users’　location　privacy　in　the　meantime.　Syntactic-based　privacy　models　have　been　widely　used　in　most　of　the　existing　location　privacy　protection　schemes.　Whereas,　they　are　suffering　from　background　knowledge　attacks,　neither　do　they　take　the　continuous　time　stamps　into　account.　Therefore　we　propose　a　new　differential　privacy　definition　in　the　context　of　location　protection　for　the　VANETs,　and　we　designed　an　obfuscation　mechanism　so　that　fine-grained　locations　and　trajectories　will　not　exposed　when　vehicles　request　location-based　services　on　continuous　time　stamps.　Then,　we　apply　the　exponential　mechanism　in　the　pseudonym　permutations　to　provide　disparate　pseudonyms　for　different　vehicles　when　making　requests　on　different　time　stamps,　these　pseudonyms　can　hide　the　position　correlation　of　vehicles　on　consecutive　time　stamps　besides　releasing　them　in　a　coarse-grained　form　simultaneously.　The　experimental　results　on　real-world　datasets　indicate　that　our　scheme　significantly　outperforms　the　baseline　approaches　in　data　utility.　©　Springer　Nature　Switzerland　AG　2018.