Abstract This study is an investigation of the effect of the delay neutron on the kinetics in the subcritical system. And, it proposes a method necessary for the kinetics code development that uses the Monte Carlo (MC) computation. It is generally difficult to analyze three dimensional space and time dependent kinetics by using a MC method. It is because the sampling of the neutron in a region becomes difficult when conditions of the region changes with time. In this study, we consider about the effect of delayed neutron in the kinetics of ADS. The behavior of neutrons is considered spontaneous in this system. It means a neutron is absorbed or leaks in a short period, while the conditions of region do not change. Therefore they are treated by steady state calculation. On the other hand the densities of delayed neutron precursors changes slowly, and the conditions of region change. In the concept of developed MC method, the neutrons are calculated by using steady state equation at each time point, and the delayed neutron precursors are calculated by using time dependent equation. We tried to inspect the accuracy of this method by using a point equation. We obtained strict solution Φ* as a reference solution, Φ1 as a solution by the present method, and Φ2 as the solution where both neutrons and delayed neutron precursors are treated by using static equations. The obtained results show a good agreement between Φ1 and Φ*, though the Φ2 agrees with Φ* poorly in all cases. Especially, we showed that this technique was effective from the reactivity change by ADS, and the relation of a delayed neutron. Finally, the effect of the delay neutron on the beam trip in the neutron source for the drive was examined by using the technique of Φ2.