In this article, the critical behavior of birth-death equation for trimolecular reactionmodel has been discussed. If 1+k3A23D1)/D2)1/2]2, it is just the critical behaviorof the trimolecular model itself. The amplitudes of the unstable fluctuation waves have been taken as order parameters describing the change of fluctuation distribution near the critical point (B=Bm). By using the renormalization method to evade the difficulty due to the divergence of the fluctuation of steady solution at Bm, we obtain the generalized Landau-Ginzburg equations for the amplitudes of average values and fluctuation of partical numbers.The analytical and numerical analysis show that, as B increases beyond Bm, the variance also has a periodical stable part, the amplitude of which is very large and determined mainly by the saturated amplitudes of average particle numbers.