The compressible flow of reactive fluid is investigated by using the transonic small-disturbance (TSD) model and the one-step first-order Arrhenuis chemical reaction. The fluid flow is restricted to dilute premixed reactions with small heat release. The effects of channel shape and Mach number on transonic combustion are studied by numerical analysis. The results show that the channel divergence increases the chemical reaction within the given channel length whereas the channel convergence inhibits the chemical reaction near the outlet and that increasing the inlet flow Mach number at a fixed reaction rate causes the flow acceleration in a diverging channel and the appearance of weak shock waves which do not show in the inert flow case. It also helps to increase the pressure and temperature near the diverging channel outlet and to consume the reactant within the given channel length.