The invention relates to a four-pointed star-shaped single-action piston cylinder offset type radial plunger motor. A main housing (18) is provided with four uniformly distributed plunger cylinders, the axis of each of the plunger cylinders has an offset (H) to the center line of a crankshaft (15), one end of a plunger (11) is a bulb in structure, the bulb of the plunger (11) is provided with a sliding shoe (13), the sliding shoe (13) is provided with a block (12) composed of two semicircles, the sliding shoe (13) on the outboard of the block (12) is provided with a spring clasp (7), the plunger (11) and the sliding shoe (13) are connected into one body through the spring clasp (7) and the block (12) to limit the bulb of the plunger (11) to rotating in a ball socket, the other end of the sliding shoe (13) contacts with the excircle of the eccentric wheel of the crankshaft (15), and the left end and the right end of the sliding shoe (13) are provided with retainer rings (17, 17') respectively to hoop the sliding shoe (13) on the surface of the excircle of the eccentric wheel of the crankshaft (15) and make the sliding shoe (13) slide on the surface of the excircle of the eccentric wheel of the crankshaft (15).