For the effective utilization of recycled aggregate concrete (RAC), it is necessary to correctly describe its compressive stress-strain curve (SSC) in theoretical and numerical analysis as well as engineering design of RAC structures. The objective of this study is to establish a good mathematical model for SSC of RAC. Based on energy dissipation theory, the differential governing equation of SSC is deduced and a new mathematical model is obtained. The new model can well describe both hardening type SSC and softening type SSC. It can overcome the shortcoming of the traditional model. Finally, good agreements have been found between the new model and the experimental investigations.