With　the　explosive　growth　of　data　volume　in　the　cloud　computing　environment,　data　owners　are　increasingly　inclined　to　store　their　data　on　the　cloud.　Although　data　outsourcing　reduces　computation　and　storage　costs　for　them,　it　inevitably　brings　new　security　and　privacy　concerns,　as　the　data　owners　lose　direct　control　of　sensitive　data.　Meanwhile,　most　of　the　existing　ranked　keyword　search　schemes　mainly　focus　on　enriching　search　efficiency　or　functionality,　but　lack　of　providing　efficient　access　control　and　formal　security　analysis　simultaneously.　To　address　these　limitations,　in　this　article　we　propose　an　efficient　and　privacy-preserving　Multi-keyword　Ranked　Search　scheme　with　Fine-grained　access　control　(MRSF).　MRSF　can　realize　highly　accurate　ciphertext　retrieval　by　combining　coordinate　matching　with　Term　Frequency-Inverse　Document　Frequency　(TF-IDF)　and　improving　the　secure　kNN　method.　Besides,　it　can　effectively　refine　users＇　search　privileges　by　utilizing　the　polynomial-based　access　strategy.　Formal　security　analysis　shows　that　MRSF　is　secure　in　terms　of　confidentiality　of　outsourced　data　and　the　privacy　of　index　and　tokens.　Extensive　experiments　further　show　that,　compared　with　existing　schemes,　MRSF　achieves　higher　search　accuracy　and　more　functionalities　efficiently.