The triple-shear unified structured constitutive model is proposed for the undisturbed saturated clay in normal consolidation based on the disturbed state concept, in which the relative intact state is characterized by the non-linear elastic model, and the fully adjusted state is characterized by the elasto-plastic model built with the combination of the triple-shear unified failure criterion and the modified Cam-clay model in the critical state soil mechanics. The coordinate translation is presented to describe the influences of the cohesion on the soil mechanical properties better. The proposed model can overcome the shortcomings of the modified cam-clay model with the definite failure stress ratio without considering the soil cohesion, which can't reflect the practical differences of strength properties under different stress states and soil cohesion. The advantage is that the new model could show the practical effects under the different stress states acting on the saturated structured clay with different cohesion better. It is shown that it can describe the effects of intermediate principal stress, rang changes of stress and difference between tension and compression. In order to verify the model proposed here, comparisons between the numerical simulations and experimental results under conventional tri-axial compression to the Jiangxi undisturbed lateritic clay was made,which results show that the proposed model could reflect the mechanical and deformation characteristics of the Jiangxi undisturbed lateritic clay well.