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This paper presents a task space coordination controller for the parallel manipulators with actuation redundancy to improve the motion relation between multiple kinematic chains. According to the mechanism characteristic of multiple kinematic chains, two different types of synchronization error are developed in the joint space of active joints and in the task space of end-effector, respectively. The coordination controller is designed by using the synchronization error, and it is proved to guarantee asymptotic convergence to zero of both tracking error and synchronization error with the Barbalat's Lemma. The trajectory tracking experiments are carried out on an actual parallel manipulator with actuation redundancy, and the superiority of the coordination controller over the traditional augmented PD (APD) controller is studied.