Abstract: At present, the stress-strain curve of loess can only be described by using different mathematical models according to its morphological type. To achieve a unified description of the stress-strain mathematical model, a new nonlinear model is proposed, and the method for determining each parameter is also given. The various types of stress-strain curves of structural loess which are obtained from conventional triaxial tests are simulated by applying the new model and the current main nonlinear models (Duncan-Chang hyperbolic model, exponential model and model of camelback curve), and then they are compared with the measured stress-strain data points. The result shows that the expression of the new model can make a more accurate description for the softening stress-strain curve than that of the hump curve. Similarly, the new model describes the hardening stress-strain curve more accurately in comparison with the Duncan-Chang hyperbolic model and the exponential model, which indicates that the new nonlinear model can describe the strong hardening stress-strain curve and the weak hardening curve, and can also describe the strong softening curve and the weak softening curve. Meanwhile, based on the description of stress-strain curves of the classic example by the new model, it is shown that the new model has excellent adaptability. The proposed model provides a unified mathematical model for the stress-strain curves of different shapes.