Abstract: The stiffness of point kinetics is very strong, while it usually takes a lot of time to solve by using full implicit Runge Kutta（FIRK）. Diagonally Implicit Runge Kutta（DIRK） is a useful tool like FIRK to solve the stiff differential equations, while it greatly reduces the computation compared with FIRK. By embedded lower order Runge Kutta, the time step-size adaptation technique is implemented, which improves the computation efficiency of DIRK. Through three typical cases with step, ramp and sinusoidal reactivity insertions, it shows that the results obtained by DIRK are in good agreement with other available results and DIRK can give far more accurate results than θ method at the same computation cost, especially in the case of fast ramp reactivity insertion.