By adding copper to increase the performance, the Ni-Ti-Cu Shape Memory Alloy (SMA), has been widely used in the field of engineering in recent years. A thermodynamic constitutive model for Ni-Ti-Cu SMA considering different copper contents is established in this work. Numerical results for two different copper contents, as examples, are compared with the experimental results to verify the accuracy of the theoretical work. Based on the verified constitutive model, the effects of different copper content on the mechanical properties of Ni-Ti-Cu SMA and the tensile and compressive asymmetric properties of Ni-Ti-Cu SMA are finally discussed, respectively.