A windshield glass support structure includes a windshield glass (1), a lower end support member (3) supporting a lower end portion of the windshield glass, and a dynamic damper (7) provided at a position corresponding to a resonance antinode of the lower end support member. The dynamic damper is an additional vibration system including an additional spring and an additional mass with respect to a main vibration system in which a glass support rigidity of the lower end support member is a main spring and the windshield glass is a main mass. A resonance frequency of the dynamic damper is set in a frequency band in which the additional mass vibrates in an antiphase with respect to a vibration phase in which the lower end portion of the windshield glass vibrates in a resonance node in a front-back direction of the vehicle caused by a vibration input.