We analyze the stability of linearly chirped Gaussian pulse stacking (LCGPS) in the laser plasma reaction (LPR) in the inertial confinement fusion (ICF) system. The LPR can be treated as the process that the stacked pulse is first intensity filtered and then induces the plasma due to the thermalization time of the plasma. We also examine the stability of LCGPS over the change of the thermalization time of the plasma, the timing delay, and the intensity attenuation of the stacked pulse in the LPR, and compare the results with those of none chirped Gaussian pulse stacking (NCGPS). Our results show that LCGPS is more stable than NCGPS.