The complete constitutive relationship curve of concrete is the key basis for the analysis of nonlinear behavior and the collapse process of concrete structures under earthquakes. However, the existing experimental measures only yield the strength and the modulus of elasticity of concrete, and the correlation between them is not reasonably quantified. This is inadequate for the determination of complete constitutive relationship curve of concrete. Based on the damage constitutive model of concrete, the compressive strength, peak strain, modulus of elasticity and the parameter of descent stage are identified from the tested data of complete uni-axial compressive stress-strain curves of concrete by adopting the best square approximation criterion and the genetic algorithmFurthermore, the marginal distribution of the above parameters and the dependence between them are studied. The optimal marginal distribution and Copula model are determined by the goodness-of-fit test. Furthermore, the conditional sampling method is employed to generate samples of the 4 probabilistically dependent parameters to construct the calculated constitutive curves. The results show that only when the probabilistical dependence between the constitutive parameters of concrete are reasonably characterized, can the mean and standard deviation of the complete compressive stress-strain curves agree well with the test results. The investigation will provide a reasonable basis for the nonlinear response analysis of concrete structures.