The progress on combustion catalysts of solid propellants in recent years was reviewed. The characteristics and development direction of combustion catalysts, such as metal, metallic oxide, composite metallic oxide, organo-metallic compounds, energetic catalyst and new carbon materials as well as the application investigation of quantum chemical calculation in combustion catalysts were summarized. It can be seen that the combustion catalysts have been developed from common single catalysts to nano-composite ones and from inert catalysts to energetic ones. Quantum chemical calculation can be used to study the catalytic mechanism, predict and calculate the structure and property of catalysts, and guide the synthesis of combustion catalysts and their applications. Considering that green environment protection is the theme of social development and the energetic catalysts possess dual advantages of energy and nanometer, investigation of the design and synthesis of green and insensitive composite energetic catalysts through quantum chemical calculation shall become the research focus of combustion catalysts in the future.