A connecting structure includes: a molding having a fixed portion that is fixed on an inner surface of a lower edge of a windshield glass, and a fitting portion that receives an engagement rib that protrudes downward from a location near an upper edge of a cowl louver, wherein the engagement rib and the fitting portion include slip-out prevention projections that prevent the engagement rib from slipping out. On both sides of the engagement rib are provided elastic lips and that are supported by the fitting portion, and these elastic lips extend in the extending direction of the engagement rib and press on the engagement rib at a side closer to a tip of the engagement rib than the slip-out prevention projections, these elastic lips press each other in opposite directions.