With the rapid development of science and technology as well as increasingly fierce competition in product manufacturing, the accurate prediction, and precise control of bending springback have been the key issue to solve. Springback is the most common metal forming phenomenon. In the past few decades, a lot of research work was concentrated in the plane pure bending of straight beam. This paper made the plane curved beam with any cross-section as studying object, carried out a systematic theoretical study based on the unloading law of classical elastic–plastic theory and the characteristic of strain superposition. The theoretical derivation was built on basic assumptions which are widely applicable. The plane bending geometric constraint equation and the springback equation were established. The springback theory of plane bending was built. The springback theory was used to these techniques as expanding roundness setting, compression roundness setting, over-bending roundness setting, large pipe straightening, and profile stretch-bending. The analytic results and the results obtained by computer numerical simulations and physical experiments agreed well. The theory not only further enriches the content of the classical theory of elastic–plastic bending, but also provides a theoretical basis and technical support for the springback prediction in engineering problems.