In this link actuation device, arms of a plurality of link mechanisms are driven to be rotated by actuators, whereby the posture of a distal end side link hub is changed. A divided section setter divides a trajectory on a work surface on which an end effector works, into a plurality of sections at pass points and sets the sections. An arm rotation speed calculator calculates a rotation speed at which each arm performs constant speed rotation in each section on the basis of: a time period of movement in the section which is determined from a target moving speed and the distance of the section; and a rotation-angular movement amount of the arm in the section. A posture change controller performs positioning control on each actuator so as to cause its corresponding arm to continuously rotate at the corresponding rotation speed without acceleration/deceleration.