In　order　to　perform　the　collision　avoidance,　a　new　algorithm　is　introduced　to　make　use　of　the　high　effectiveness　of　GPU　to　compute　the　discrete　Voronoi　diagram　in　real-time.　And　a　solution　for　crowd　path　navigation　based　Voronoi　diagram　is　presented.　By　making　use　of　the　ability　that　the　Voronoi　diagram　partitions　the　space　according　to　the　Euclidean　metric,　the　path　planning　with　collision　avoidance　is　achieved　by　forbidding　agents　to　move　outside　their　Voronoi　regions.