Mathematical model for soil stress-strain curve is very important to theory study of soil mechanics and numerical simulation of corresponding geotechnical engineering; however it is not well solved. Based on experimental data of Yangtze River soil, shortcoming of traditional hyperbolic stress-strain model is pointed out. Composite two-segment hyperbolic model (CTH model) and composite hyperbolic-line model (CHL model) are presented to describe harden type and soften type stress-strain curves, respectively. These two improved models both can be simplified into hyperbolic model with their special parameters. Finally, one harden type and two soften type curves are put forwarded in order to validate the accuracy of CTH model and CHL model, and good agreements have been found between experimental curves and fitting results of the improved models. The results of this study put good foundation for numerical simulation and design of corresponding geotechnical engineering.