The main challenges in designing a small-size combustor operating at relatively high throughflow speeds are the insufficient space for mixing and burning due to the short residence time of mixtures and the difficulties in flame stabilization. In this study, the trapped vortex combustor (TVC) concept is investigated because it provides a more stable way for mixing and flame holding by holding the pilot flame inside a cavity instead of exposing it to the mainstream. The computations are performed using a well-validated flow solver with appropriate models for turbulence, species transport and combustion. Three main parts are studied including the flow field characteristics of the combustor without fuel injection; the effects of fuel injection, mixing and penetration without combustion; and the combustion process. The optimum cavity configuration in the cold flow, the mixing efficiency, the total pressure and the combustion efficiency are considered in these parts. The results show that TVC provides a good overall performance for the designed combustor and also has the potential to be compact. This paper represents a contribution to understand the capability and working processes of trapped vortex combustors for high speed flows.