The invention discloses a sharp-vertex dual-sweepback osculating-cone wave rider with transition sections. Each front edge of the wave rider consists of two straight sections and a transition curve for connecting the two corresponding straight sections; from a sharp vertex, each first straight section corresponds to a first sweepback angle, and each second straight section corresponds to a second sweepback angle; the angle of the two sweepback angles are controllable in a designing stage; and each transition curve is used for connecting the two corresponding straight sections, and enabling a first-order derivative and a second-order derivative to be continuous. Through the adoption of the wave rider disclosed by the invention, the sweepback effect of the wave rider can be effectively utilized to generate a stable separation vortex similar to a double-delta wing on the upper surface of the wave rider, and the plane area of the wave rider is enlarged by dual-sweepback front edges, so that the lifting force of the wave rider can be increased to a large extent, and the volumetric efficiency does not need to be reduced; the angle of the second sweepback angle is small, and the effect of the second sweepback angle is similar to the effect of the double-delta wing, so that improvement of the low-speed performance of the wave rider is facilitated; and the situation that the front edges of two sweepback parts are in first-order derivative continuity in geometry is guaranteed by the transition sections.