The unloading spring-back of tubes during its manufacturing process shows a strong nonlinearity, which greatly influences the precision of parts. In this paper, the strain distribution of bending tubes was analyzed based on the elasto-plasticity theory, and the theoretical equation for spring-back of tubes was derived. The numerical simulation model for cold tube-bending process was developed with prediction error of 9% compared with experimental results, indicating high reliability of the model. The 12Cr1MoV and 20G tubes were used to analyze the effects of bending angle, bending radius and bending speed on the spring-back of tubes. The prediction equation of spring-back was built, which shows that the spring-back tendency was in accordance with theoretical analysis results. The simulated results show that the spring-back angle is linearly proportional to the bending angle within a certain range. In addition, it is proportional to the relative bending radius and the bending speed.