A　major　shortcoming　of　the　conventional　car-following　models　is　that　these　models　only　consider　the　current　spacing　and　speeds　of　the　target　vehicle　and　its　immediate　leading　vehicle,　without　taking　into　account　prior　driving　actions,　even　for　those　from　the　same　driver.　In　other　words,　the　numerous　prior　experiences　have　no　influence　in　predicting　vehicular　movements　for　the　next　time　step.　In　this　research,　we　propose　a　machine-learning-based　data-driven　methodology　that　is　able　to　take　advantage　of　the　high-resolution　historical　traffic　data　in　the　current　data-rich　era,　to　predict　vehicular　movements　in　an　accurate　manner　with　high　computational　efficiency.　The　proposed　car-following　model　has　a　simple　model　structure　based　on　a　fixed-radius　near　neighbors　(FRNN)　search　algorithm　and　it　can　be　applied　to　high-resolution,　real-time　vehicle　movement　prediction,　modeling,　and　control.　A　comprehensive　performance　comparison　is　also　conducted　among　the　proposed　car-following　model,　another　similar　data-driven　model,　and　two　conventional　formula-based　models.　The　results　indicate　that　the　FRNN　algorithm-based　car-following　model　is　superior　to　all　other　three　models　in　terms　of　prediction　accuracy　and　is　more　computationally　efficient　compared　to　its　data-driven-based　counterpart.　Some　extensive　applications　of　the　proposed　car-following　model　are　also　discussed　at　the　end　of　this　article.