The invention discloses a rocking pneumatic impact machine, and belongs to the coal washing and dressing industry. The rocking pneumatic impact machine is used with an arc-shaped classifying screen and comprises an electric control portion, an actuation cylinder, a rocker arm and the like. The rocker arm is a self-balanced rocker arm with symmetric equal armed levers and comprises impact head assemblies, impact rods and a rocker arm body, the middle of the rocker arm body is connected with a base by a hinge pin, two ends of the rocker arm body are respectively connected with the impact rods and the impact head assemblies, the impact head assemblies and the impact rods are symmetrically arranged, and the weight of the rocker arm body is in a self-balanced state around the hinge pin; the electric control portion is connected with the cylinder, and the cylinder is connected with the rocker arm body. The rocking pneumatic impact machine has the advantages that the rocker arm is of a balance scale structure, the stroke of the cylinder is enlarged, the impact speed is increased, the dead weight of the rocker arm is in the self-balanced state, and the rocking pneumatic impact machine can swing flexibly and is low in resistance; a cylinder driving portion is in a design of a surpassing structure with free stroke, so that a quick rebounding effect can be realized after impact actions are completed, elastic impact actions can be implemented, and the impact efficiency can be improved; the rocking pneumatic impact machine can be repositioned flexibly and conveniently owing to hoop locking structures of the impact head assemblies, so that multiple points can be impacted precisely.