In a windshield glass support structure, a lower end of a windshield glass is supported at an upper end of a cowl portion across the entire width in the vehicle width direction. The cowl portion is open toward the front of a vehicle body with a cowl outer which forms an upper portion of the cowl portion and a cowl inner which forms a lower portion of the cowl portion. Braces which form a closed cross-section with the cowl portion connect the cowl outer with the cowl inner at positions dividing the cowl portion into three substantially equal parts in the vehicle width direction.