Geometric　model　fitting　has　been　widely　used　in　many　computer　vision　tasks.　However,　it　remains　as　a　challenging　task　when　handing　multiple-structural　data　contaminated　by　noises　and　outliers.　Most　previous　work　on　model　fitting　cannot　guarantee　the　consistency　of　their　solutions　due　to　their　randomness,　precluding　them　from　many　real-world　applications.　In　this　research,　we　propose　a　fast　two-view　approximately　deterministic　model　fitting　scheme　(called　LGF),　to　provide　consistent　solutions　for　multiple-structural　data.　The　proposed　LGF　scheme　starts　from　defining　preference　function　by　preserving　local　neighborhood　relationship,　and　then　adopts　the　min-hash　technique　to　roughly　sample　subsets.　By　this　way,　it　is　able　to　cover　all　model　instances　in　data　in　the　parameter　space　with　a　high　probability.　After　that,　LGF　refines　the　previous　sampled　subsets　by　global-residual　optimization.　Furthermore,　we　propose　a　simple　yet　effective　model　selection　framework　to　estimate　the　number　and　the　parameters　of　model　instances　in　data.　Extensive　experiments　on　real　images　show　that　the　proposed　LGF　scheme　is　able　to　observe　superior　or　very　competitive　performance　on　both　accuracy　and　speed　over　several　state-of-the-art　model　fitting　methods.