A three-plane-branch six-degree-of-freedom parallel wall-climbing robot mainly comprises a movable platform, a laser gun, three plane branches, a reset mechanism and three traction legs. Each plane branch comprises two telescopic driving legs, the upper end of each driving leg and the movable platform are in composite universal pair connection through a transverse shaft, and the lower end of each driving leg and a permanent magnetic chuck are in composite ball pair connection. The traction legs can stretch out in a rigidity mode, retract in a flexibility mode and swing, the upper end of each traction leg and the movable platform are in ball pair connection, and the lower end of each traction leg and a permanent magnetic chuck are in ball pair connection. The reset mechanism enables the plane branches to be reset through the transverse shafts. Pressing springs enable the traction legs to be reset, all the legs and the permanent magnetic chucks are in coordinated movement, and wall face climbing of magnetic workpieces is achieved. After absorbing and positioning are completed, the absorption capacity of the chucks acts on the movable platform all the time, the wall-climbing robot is changed into a parallel robot, and the movable platform drives the laser gun so that large equipment can be repaired and workpiece defects can be overcome. The three-plane-branch six-degree-of-freedom parallel wall-climbing robot has the advantages of being simple in structure, strong in absorption capacity, flexible to move, simple in control, low in self weight, and capable of achieving the dual functions of quick translation wall climbing and large-load six-degree-of-freedom flexible operation.