A non-circular stator internal ring curve single-acting vane pump belongs to the field of mechanical design in mechanical engineering, which is a hydraulic pump that the vane is geometrically sealed with the stator and that the vane is tightly jointed with the internal surface of the stator without external force. The stator internal ring curve in the invention is a non-circular closed curve: any straight line is made through the acnode of the non-circular closed curve, the length of the line segment formed by two intersection points of the straight line and the non-circular closed curve is always a definite value, and the polar equation of the non-circular closed curve is as follows: rho equals R plus F (theta); in the formula, rho is polar radius, theta is polar angle, R is constant; and in rectangular coordinate system, F (theta) is continuous periodic function and is symmetrical about the point (phi, 0), the cycle time T is equal to 2 phi, and theta belongs to (0, 2 phi). Compared with the existing vane pump, in the working process of the non-circular stator internal ring curve single-acting vane pump in the invention, the vane radial force is balanced without supplying high pressure oil through the root of the vane groove, that is, oil supply path is not needed; and the pump is simple in structure, and the manufacturing technology is convenient. The non-circular closed curve further can be used for vane hydraulic motors.