A frameless glass door clamp has a clamping member, a base cover and a cap cover. The clamp member has a base side surface and a cap side surface. The base cover is mounted on the base side surface and has a panel, multiple flanges, a tapered face and multiple rounded outer edges. The cap cover is mounted on the cap side surface and has a panel, a multiple flanges, a tapered face and multiple rounded outer edges. Because the outer edges of the base and cap covers are rounded, the frameless glass door clamp is much less likely to injure people or damage objects and is easier to manufacture.