In this paper, the method of limit analysis is adopted, and three kinds of self-bending extrusion dies controlled by combined function are presented. They are the sin-atan self-bending extrusion die, the sin-erf self-bending extrusion die, and the sin-tanh self-bending extrusion die. Through numerical simulation, self-bending profiles can be obtained from all three kinds of dies. These dies can make the billet flow closer to the real billet flow path and maximize the billet utilization rate. They also can reduce the extrusion load and reduce the local damage of the die and then prolong the die life. It is very effective to predict the bending deformation of the billet by analyzing the central flow line of the billet. It provides a theoretical reference for the design of the actual streamlined self-bending die.