Inthispaper,someteststatisticsOfKolmogorovtypeandCramervonMisestypebasedonprojectionpursuittechniqueareproposedfortestingthesphericityproblemofahigh-dimensionaldistribution.Thelimitingdistributionsoftheteststatisticsarederivedunderthenullhypothesis.TheasymptoticpropertiesofBootstrapapproximationareinvestigatedandthetailbehaviorsofthestatisticsarestudied.