The utility model discloses a clamp for beveled edges at arbitrary angles. The clamp comprises a support, a chuck, a rotary shaft, a rotary shaft housing, a locking structure of the rotary shaft used for fixing the rotary shaft and a double-surface angle graduated disc. The chuck is fixed at one end of the rotary shaft which rotatably sleeves the rotary shaft housing. The double-surface angle graduated disc is fixedly connected at the other end of the rotary shaft. A boss is arranged on the support and provided with a groove at the end portion. The rotary shaft housing is provided with a circular boss in a radial direction. The circular boss cooperates with and rotates relatively to the groove. The clamp further comprises a plane angle-adjusting structure used for adjusting rotating angles formed between the boss of the support and the circular boss of the rotary shaft housing. The clamp for the beveled edges at the arbitrary angles has following beneficial effects: the clamp is capable of rotating around two coordinate axes including an X axis and a Y axis so that the problem of tedious alignment angles is resolved; and a pipe fitting can be placed at arbitrary angles and the beveled edges at the arbitrary angles can be machined in combination with wire-cutting machining technology or a milling machine so that production efficiency is substantially boosted.