Precise　localization　is　an　essential　issue　for　autonomous　driving　systems.　2D　LiDAR　has　been　widely　used　in　various　indoor　localization　systems　because　of　its　accuracy　in　measuring　distances.　However,　the　data　of　2D　LiDAR　in　the　outdoor　environment　is　very　sparse　and　affected　by　dynamic　objects　greatly,　which　makes　it　very　difficult　to　find　the　corresponding　points.　To　overcome　this　defect,　we　propose　a　novel　outdoor　localization　framework　based　on　the　fusion　of　stereo　vision　and　2D　LiDAR,　called　FVL-OutLoc.　This　framework　first　adopts　Dempster-Shafer　theory　to　fuse　several　consecutive　frames　of　2D　LiDAR　data　into　a　grid　submap　by　using　stereo　odometry.　Finally,　Fourier-Mellin　Transform　is　chosen　to　match　the　submap　and　prior　map　for　further　correcting　the　odometry.　The　experimental　results　on　the　KITTI　dataset　show　that　FVL-OutLoc　can　achieve　high　localization　accuracy　and　run　at　a　real-time　performance.　©　2021　IEEE