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We propose the mechanism and control method of the air jet based parallel link actuator with 6 degrees of freedom. The rotor of the actuator is called a platform which is constructed by connecting multiple spheres that are located in vertex of a regular polygon with high rigid wires. Each sphere is spatially levitated using coanda effect and its 3D position is feedback controlled by the dedicated air jet driven by a pan-tilt motor on the stator of the actuator. First, we discuss the platform structure in which n spheres are arranged at the vertices of a regular polygon, and the kinematics and control of the parallel link mechanism in which each sphere is operated by one of n air jet nozzles arranged in the same structure as the platform. Then we created an experimental system using the case of the minimum number n = 3, implemented a control system based on the inverse kinematics, and conducted operation experiments. The basic validity of the proposed method was confirmed by evaluating the experimental results obtained from an external measuring system which can accurately calculate the position and the orientation of the platform.