The invention discloses a fluid damping device used for coping with pipeline pressure jump. The fluid damping device comprises a box body. The box body is in a shape like a rotation body, wherein an ovoid curve rotates around the axis by a cycle to form the rotation body; and the two ends of the box body are coaxially provided with an outlet, an inlet and a connecting device for connecting an upstream gas pipeline with a downstream gas pipeline. Multiple groove pipes pointing to the outlet are evenly distributed on the inner wall, close to the outlet, of the box body in a spaced manner in a peripheral direction. The radian of the groove pipes is consistent with that of the inner wall of the box body. A plastic ball is smooth in surface and is movably placed in an inner cavity of the box body. The diameter of the plastic ball is larger than the diameter of the upstream gas pipeline and the diameter of the downstream gas pipeline. By changing the circulation area and the local resistance coefficient, the response time of downstream pressure jump is prolonged, the purpose that pressure is adjusted slowly is achieved, the structure and the principle are simple and clear, the fluid damping device is easy to mount and maintain, sensitive to response and fast in adjustment, the influence of upstream pressure jump on downstream pipeline instruments and equipment is relieved, the operating cost of enterprises is lowered, and safe and stable operation of the pipelines is guaranteed.