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 an electrostatic pressure which, working together with the thermal pressure, would counter the gravitational collapse. As a result, the effective Jeans length, lambda[over ]_{J} is increased by a factor lambda[over ]_{J}/lambda_{J}=sqrt[8/5], relative to the conventional one. For scales smaller than the effective Jeans scale the plasma would oscillate at the ion-acoustic frequency. The modes that would be influenced by this effect lie roughly in the range 0.5h Mpc;{-1}<k, which corresponds to the Lyman-alpha forest from the intergalactic 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} approximately 1-(5/6);{2} approximately 30%.