A windshield glass peripheral structure is provided including a molding that couples a windshield glass with a cowl louver. The molding includes an attachment portion that is attached to an inner side of an upper end portion of the cowl louver, an interposing portion that is interposed between and seals between a lower end portion of the windshield glass and an upper end portion of the cowl louver, and has a leading end at a vehicle outer side making contact with a lower edge portion of the windshield, glass, and a joining portion. The joining portion extends in a vehicle width direction following, the lower end portion of the windshield glass, is formed with a water drainage portion cut out from a vehicle up-down direction upper end portion of the joining face further toward a vehicle width direction outer side than a wiper unit.