Inthispaper,usingpseudo-holomorphiccurvemethod,oneprovestheWeinsteinconjectureintheproductP_1×P_2oftwostronglygeometricallyboundedsymplecticmanifoldsundersomeconditionswithP_1.Inparticular,ifNisaclosedmanifoldoranoncompactmanifoldoffinitetopologicaltype,ourresultimpliesthattheWeinsteinconjectureinCP~2×T*Nholds.