In this paper, the dispersion controlled dissipative (DCD) scheme is reviewed and then extended to simulate chemically reacting gas flows in multicomponent mixtures in the presence of strong shock waves. Furthermore, the properties of the reactive DCD (DCD-R) scheme are discussed, followed by several applications. The DCD scheme has been shown to have the following features: high accuracy and robustness for reacting gas flows in the presence of strong shock waves and contact discontinuities, and algorithmic simplicity.