This paper presents a new magnetic levitation system, MagTable, which provides six-degrees-of-freedom (6-DOF) and completely contactless operation of a magnetized object. The MagTable consists of a planar array of square coils and a permanent magnet type carrier. The maximum levitation height of the carrier is 30mm within a 400mm × 200mm horizontal translation range. The novelty of this research lies in the fully untethered manipulation of levitated carriers in such a large area, and in the fast and accurate computation of wrench matrix using the magnetic nodes method and the Lorentz force law. In this paper, the design method is firstly provided. Then, the optimization of the carrier's magnet topology, based on better controllability and minimum power consumption, is documented. Experimental results of the 5-DOF motion control of two single-permanent-magnet carriers and the 6-DOF motion control of a three-permanent-magnets carrier are presented. The results demonstrate the performance of the MagTable in 100mm × 40mm horizontal translation range with maximum levitation height of 20mm. The rotation range are ±6° in both roll and pitch, and ±12° yaw motion about the vertical axis. The proposed system has potential applications in fast and high precision manipulation tasks.