Starting from the kinetic equation in the K space, which is the Fourier space of velocity V and using the technique of operator calculation and transformation, the re-normalized dispersion equation of turbulent plasma has been deriv ed rather simply. The effect of finite correlation time of the turbulence has been calculated under the approximation of assuming a turbulence with effective correlation time τeff instead of the one with time and space correlation. It shows that the effect of finite τeff will reduce the effect of turbulence. Therefore, the expression obtained in the limiting case of short eorrelation time is the upper bound of the turbulence effect. The effects of turbulence on the ion sounds, electron langmuir waves and drift waves have also been discussed.