  We point out that during the reionization epoch of the cosmic history, the
plasma collective effect among the ordinary matter would suppress the large
scale structure formation. The imperfect Debye shielding at finite temperature
would induce a residual long-range electrostatic potential which, working
together with the baryon thermal pressure, would counter the gravitational
collapse. As a result the effective Jean's length, $\tilde{\lambda}_J$, is
increased by a factor, $\tilde{\lambda}_J/\lambda_J=\sqrt{8/5}$, relative to
the conventional one. For scales smaller than the effective Jean's scale the
plasma would oscillate at the ion-acoustic frequency. The modes that would be
influenced by this effect depend on the starting time and the initial
temperature of reionization, but roughly lie in the range $0.5 h{\rm Mpc}^{-1}<
k$, which corresponds to the region of the Lyman-$\alpha$ forest from the
inter-galactic medium. We predict that in the linear regime of density-contrast
growth, the plasma suppression of the matter power spectrum would approach
$1-(\Omega_{dm}/\Omega_m)^2\sim 1-(5/6)^2\sim 30%$.
