Abstract： On the basis of the Oregonator model, we took the rate constant k6, the stoichio-metric coefficient f and the wave number k as the parameters to study the stability of the BZ reaction system. The expressions of the following physical quantities were obtained, they included: the critical rate constant k6c of the space periodic structure, its short-wavelength critical wave number ksc and long-wavelength critical wave number kLc; the critical rate constant k6c of time-space periodic structure and its critical wave number kc(kc = kLc). Then we worked out the critical frequency λc of BZ reaction system and analyzed the near-by critical state behavior of the system, whereby we obtained the trigger wave velocity ur and phave wave velocity up. We came to the conclusion that, under certain conditions, the near-by critical state of unstirred BZ reaction system may exhibit a stable wave group, or, a wave packet.. The trigger wave is a wave packet in the homogeneous system and the phase wave is a wave packet in the inhomogeneous one with a slight gradient. We have got that (uT=2ηDkc, where D is the diffusion coefficient of HBrO2,η changes slowly with [H+] (to the extent of experimental observation, η≈ 0.1), and UP = v, where v is the phase velocity.