A premixed-compression-ignition engine has been studied to improve the efficiency and to decrease exhaust emissions. However those systems have some difficulties for controlling combustion process. Radical is an activated chemical species formed by a chemical chain reaction between reactant and product. When the chain reactions occur, the energy bond of species is broken easily by the released radicals. The combustion chamber of the premixed-compression-ingnition engine is consist of a main chamber with lean premixture and a subchamber with rich premixture. Those are connected by narrow cylinderical connections. With ignition start in the subchamber, many different kinds of radical is jetted into the main chamber. The premixed gas in main chamber is quickly burned up by the radical ignition in multi-pionts. In this paper, the combustion phenomena in a constant volume combustor having a radical injector are numerically analyzed. The some constants in the reaction rate equation are adjusted by the experimental results tested in the same geometrical chamber. The code is applied on the two combustors in a wide range of equivalence ratio. The results show that the burning time is much shorter in the combustor having radical injector.