A connecting link structure for connecting a grass cutting unit to a position between front and rear wheels of a riding type lawn mower. The link structure comprises parallel front links and parallel rear links each pivotally connected at one end thereof to a vehicle body and at the other end to the grass cutting unit. A curved bracing auxiliary link extends from the pivotal connection between the vehicle body and one of the rear links, along this rear link, and then perpendicular to the other rear link to be secured to the other rear link at a point offset from the pivotal connection between the other rear link and the grass cutting unit.