A control device for a link actuator to control each of actuators (3, 70) of the link actuator in such a manner as to change position of a distal end side link hub relative to a proximal end side link hub from a starting point position towards a terminating point position which is commanded, in which the link actuator includes three or more link mechanisms (11 to 13) that connect the distal end side link hub to the proximal end side link hub in a position-changeable fashion, each link mechanisms (11 to 13) including a proximal side end link member (11a, 12a, 13a), one end of the proximal side end link member (11a, 12a, 13a) being pivotably connected to the proximal end side link hub; a distal side end link member (11b, 12b, 13b), one end of the distal side end link member (11b, 12b, 13b) being pivotably connected to the distal end side link hub; and an intermediate link member (11c, 12c, 13c) with its opposite ends pivotably connected to the other ends of the proximal side end link member (11a, 12a, 13a) and the distal side end link member (11b, 12b, 13b), respectively, each of the link mechanisms (11 to 13) having such a shape that a geometric model of the link mechanism (11 to 13) represented by lines shows symmetry between a proximal end side portion thereof and a distal end side portion thereof with respect to a center portion of the intermediate link member (11c, 12c, 13c), and each link mechanisms (11 to 13) being provided with the actuator (3, 70) configured to change position of the distal end side link hub relative to the proximal end side link hub by rotating the proximal side end link member (11a, 12a, 13a) in the form of an arm, characterized by the control device comprising: a position change control unit configured to drive each of the actuators (3, 70) in synchronism with each other on a point-to-point basis from a starting point, which is the rotational angle of the arm (11a, 12a, 13a) when the starting point position is assumed, to a terminating point which is the rotational angle when the terminating point position is assumed; a relay position setting unit configured to compare a position changing amount of the distal end side link hub in the position change from the starting point position to the terminating point position with a predetermined amount, and configured to, in the event that the position changing amount of the distal end side link hub is larger than the predetermined amount, set one or more relay position according to a predetermined rule during the course of a position changing path for changing from the starting point position to the terminating point position and to set by determining a rotational angle which corresponds to a relay point of the rotational path of each of the arms (11a, 12a, 13a) when the relay position is assumed, the rule including: selecting two arms out of the three arms (11a, 12a, 13a) which operate during the course of changing the position from the starting point position of the distal end side link hub to the terminating point position; equally dividing the rotational path of the selected two arms; and setting the position of the remaining one arm at a position uniquely determined according to a relative positional relationship with the other two arms, wherein the position change control unit configured to perform a position control so that each of the arms (11a, 12a, 13a) simultaneously passes through the relay point set by the relay position change setting unit. a position change control unit configured to drive each of the actuators (3, 70) in synchronism with each other on a point-to-point basis from a starting point, which is the rotational angle of the arm (11a, 12a, 13a) when the starting point position is assumed, to a terminating point which is the rotational angle when the terminating point position is assumed; a relay position setting unit configured to compare a position changing amount of the distal end side link hub in the position change from the starting point position to the terminating point position with a predetermined amount, and configured to, in the event that the position changing amount of the distal end side link hub is larger than the predetermined amount, set one or more relay position according to a predetermined rule during the course of a position changing path for changing from the starting point position to the terminating point position and to set by determining a rotational angle which corresponds to a relay point of the rotational path of each of the arms (11a, 12a, 13a) when the relay position is assumed, the rule including: selecting two arms out of the three arms (11a, 12a, 13a) which operate during the course of changing the position from the starting point position of the distal end side link hub to the terminating point position; equally dividing the rotational path of the selected two arms; and setting the position of the remaining one arm at a position uniquely determined according to a relative positional relationship with the other two arms, wherein the position change control unit configured to perform a position control so that each of the arms (11a, 12a, 13a) simultaneously passes through the relay point set by the relay position change setting unit.