The invention relates to a three-chain parallel machine tool, which comprises a machine tool body, Hook hinged shafts, telescopic rods, a parallel mechanism, a translation table, a double-cross shaft and a workbench, wherein the machine tool body is provided with two Hook hinged shafts and a double-cross shaft, two upper telescopic rods are respectively assembled on the two Hook hinged shafts, the lower telescopic rod is assembled on the double-cross shaft, one end of the two upper telescopic rods and one end of the lower telescopic rod are commonly arranged on the translation table, and the parallel mechanism is arranged between the translation table and the double-cross shaft. The machine tool is in a three-chain structure, inverse kinematics solution and forward kinematics solution are explicit expressions, the calculation is simple, so no singularity or dead spot exists, no coupling exists, and because the machine tool has simple mechanism, the real-time control is easy, the operating space is large, the working is reliable, and the cost is lower.