Conventional prestack depth migration (PSDM) based on point-source shot data involves a huge number of time-consuming wave extrapolations. Areal-source prestack data generated by a synthesis procedure can provide an alternative migration scheme that is efficient and accurate. We have developed a curved-wave synthesis method to implement curved-wave PSDM technology. A base-kernel synthesis operator is defined as a relative curved source-excitation datum. A general synthesis operator is constructed by disturbing the illumination directions of a base-kernel operator. The curved wavefields are synthesized by synthesis operators and then migrated by combination with a common-shot depth-migration algorithm. Curved wavefields can be constructed according to the configuration of a geologic structure to obtain a high-quality image of the target. Curved-wave records arising from different curved-source wavefields with different illumination properties are stacked after depth migration to produce an accurate image. A synthesis operator can be designed by simulating the configuration of target structures, or by velocity constraint in a target-oriented way, to efficiently achieve a high-quality image of a complex target area. Characteristic of curved excitation surface and space-variant illumination, the method is more adaptable to a complex medium than the plane-wave technique and more efficient than shot migration. Numerical demonstrations on synthetic and real data have proved effective and given good results.