The invention discloses a suspension frame of a maglev train, which comprises two suspension modules arranged in parallel and two linear sliding platforms arranged at two ends thereof. Two linear sliding platforms at the same ends of the two suspension modules are connected through a crossbeam, and the two suspension modules can rotate relative in either direction. A connecting rod is rotatably connected with any cross beam, and the rotation axis of the connecting rod is perpendicular to the extending direction of the cross beam; Both ends of the connecting rod are provided with sheet beams extending along the longitudinal direction of the cross beam and connected with respective suspension modules, the sheet beams are inclined downward in the directions of both sides of the connecting rodand can rotate relative to the suspension modules in either direction. A spatial four-bar mechanism is formed between the sheet beam, the connecting rod, the crossbeam and the linear sliding platformof the suspension frame, and the sheet beam, the connecting rod and the crossbeam are relatively independent, the anti-rolling and decoupling abilities of the suspension frame are improved, and the curve passing ability is further improved. The invention also discloses a maglev train with the suspension frame.