The stress–strain constitutive model under uniaxial compression is a basic element and important characterization method for determining physical and mechanical properties in cement-based materials research. In this study, a stress–strain constitutive model under uniaxial compression was established, which was based on a new nano-stabilized soil (NSS) through typical mechanical tests and constitutive relationship research. The results indicate that the unconfined compressive strength (UCS) of the nano-stabilized soil was enhanced with the increase in curing period and nano-stabilizer dosage, and that the strength growth rate reaches the maximum at a 12% dosage in the tested samples. The UCS of NSS under a 12% dosage is about 10~15% higher than that of ordinary stabilized soil (SS) without nano doping, and 25~40% higher compared with grade 42.5 cement-soil. The established constitutive model could accurately describe the linear-elastic and elastic-plastic deformation characteristics of NSS under uniaxial compression, which will be conducive to revealing the curve variation law of the stress–strain process. The research results could provide scientific support for the theoretical innovation and engineering application of green environmental protection materials.