Theoretical analysis of a solar energy-powered Rankine thermodynamic cycle utilizing an innovative new concept, which uses supercritical carbon dioxide as a working fluid, is presented. In this system, a truly 'natural' working fluid, carbon dioxide, is utilized to generate firstly electricity power and secondly high-grade heat power and low-grade heat power. The uniqueness of the system is in the way in which both solar energy and carbon dioxide, available in abundant quantities in all parts of the world, are simultaneously used to build up a thermodynamic cycle and has the potential to reduce energy shortage and greatly reduce carbon dioxide emissions and global warming, offering environmental and personal safety simultaneously. The system consists of an evacuated solar collector system, a power-generating turbine, a high-grade heat recovery system, a low-grade heat recovery system and a feed pump. The performances of this CO2-based Rankine cycle were theoretically investigated and the effects of various design conditions, namely, solar radiation, solar collector area and CO2 flow rate, were studied. Numerical simulations show that the proposed system may have electricity power efficiency and heat power efficiency as high as 11.4% and 36.2%, respectively. It is also found that the cycle performances strongly depend on climate conditions. Also the electricity power and heat power outputs increase with the collector area and CO2 flow rate. The estimated COPpower and COPheat increase with the CO2 flow rate, but decrease with the collector area. The CO2-based cycle can be optimized to provide maximum power, maximum heat recovery or a combination of both. The results suggest the potential of this new concept for applications to electricity power and heat power generation.