A gliding arc plasma is a potential way to convert CO2 into CO and O-2, due to its non-equilibrium character, but little is known about the underlying mechanisms. In this paper, a self-consistent two-dimensional (2D) gliding arc model is developed, with a detailed non-equilibrium CO2 plasma chemistry, and validated with experiments. Our calculated values of the electron number density in the plasma, the CO2 conversion and energy efficiency show reasonable agreement with the experiments, indicating that the model can provide a realistic picture of the plasma chemistry. Comparison of the results with classical thermal conversion, as well as other plasma-based technologies for CO2 conversion reported in literature, demonstrates the non-equilibrium character of the gliding arc, and indicates that the gliding arc is a promising plasma reactor for CO2 conversion. However, some process modifications should be exploited to further improve its performance. As the model provides a realistic picture of the plasma behaviour, we use it first to investigate the plasma characteristics in a whole gliding arc cycle, which is necessary to understand the underlying mechanisms. Subsequently, we perform a chemical kinetics analysis, to investigate the different pathways for CO2 loss and formation. Based on the revealed discharge properties and the underlying CO2 plasma chemistry, the model allows us to propose solutions on how to further improve the CO2 conversion and energy efficiency by a gliding arc plasma.