The invention provides a symmetrical three-axle parallel main shaft head capable of rotating around a fixed point. The symmetrical three-axle parallel main shaft head comprises a moving base, a fixedbase, and three branched chains arranged between the moving base and the fixed base and with the same structures; the branched chains comprise driving motors, first branched chain rods, lead screws, moving slide blocks, second branched chain rods and hooke joints; one ends of the first branched chain rods are connected with the fixed base; the hooke joints comprise first hooke hinges arranged in the middle positions, and second hooke hinges connected with the moving base; the lead screws are mounted on the first branched chain rods; the moving slide blocks are mounted on the lead screws; one ends of the lead screws are connected with driving motors to form moving pairs; and the driving motors and the lead screws can provide degrees of moving freedom to the moving slide blocks. A cutter canrealize multi-directional fixed-point rotation around any point in a certain range of internal space of a moving platform and a fixed platform only by the parallel main shaft head structure, and canrealize multi-directional fixed-point rotation around a cutter point.