A transmission mount structure for mounting a transmission connected to an end of a transverse-mounted engine to a vehicle body includes an elastic main vibration-damping member for reducing both vibrations in a vertical direction and vibrations in a roll direction, and an elastic auxiliary vibration-damping member smaller in diameter or thickness than the main vibration-damping member and extending in a direction substantially perpendicular to the roll direction. The auxiliary vibration-damping member has a constricted portion formed at a longitudinal central portion thereof and having a smaller cross-section than any other part of the auxiliary vibration-damping member.