Many　applications　need　to　execute　Single-Source　Shortest　Paths　(SSSP)　algorithm　on　each　snapshot　of　a　time　evolving　graph,　leading　to　long　waiting　times　experienced　by　the　users　of　such　applications.　However,　these　applications　are　often　time-sensitive,　the　delayed　computation　results　can　lead　to　the　loss　of　best　decision-making　opportunities.　To　address　this　problem,　in　this　paper　we　propose　an　efficient　SSSP　algorithm　for　time-evolving　graphs,　called　V-Grouper.　The　main　idea　of　V-Grouper　is　to　avoid　the　redundant　computations　of　the　same　vertex　in　different　snapshots.　Our　experimental　results　over　real-world　time-evolving　graphs　show　that,　due　to　the　high　similarity　of　consecutive　snapshots,　the　computation　results　of　one　vertex　in　neighboring　snapshots　are　equal　with　a　high　probability.　At　the　beginning　of　computation,　V-Grouper　first　divides　all　the　versions　of　a　given　vertex　in　different　snapshots　into　vertex　groups,　where　the　computation　result　of　each　version　is　predicted　based　on　the　aforementioned　insight　of　neighboring　snapshots　having　equal　results.　The　versions　of　the　vertex　in　each　group　have　the　same　predicted　computation　result.　During　the　computation　process　for　each　vertex　group,　only　one　version　needs　to　participate　in　computation,　avoiding　a　large　number　of　redundant　computations.　Experimental　results　show　that　V-Grouper　is　up　to　64.31x　faster　than　the　state-of-the-art　SSSP　algorithm.