Solar CO2 coal gasification has some advantages such as reducing CO2 emissions and producing gaseous fuels with high quality in a clean and efficient manner. As the core component of solar thermochemical system, the vortex reactor has the advantages of being easy to realize, facilitating reactants transport and high efficiency. A three dimensional mathematical model of a 10 kW directly-irradiated solar thermochemical vortex reactor with determined design values is established. This model couples the Euler-Lagrange gas-solid two-phase flow model, the participating media radiation model, and chemical reaction kinetic models together. User defined functions (UDF) are used to present the solar flux elliptical distribution and point-focusing characteristics. The numerical results are validated by comparing with the experimental results of ETH vortex reactor. Then the effects of operational conditions such as input solar power, mass flow rate of coal particles and CO2, intake gas temperature on reactor efficiency and conversion efficiency of coal particles and CO2 are studied. The results show the increasing of input solar power has little effect on improving conversion efficiency of coal particles and CO2. Moreover, excessive solar energy input decreases reactor efficiency. The CO gathers in the front of the reactor and decreases from the opening aperture to the cavity body and the exit. The increasing of coal mass flow rate improves the conversion efficiency of CO2, and vice versa. The cavity temperature decreases and reactor efficiency increases with the rise of coal and CO2 mass flow rate.