Abstract: In this article, as the velocity gradient is taken as a constant value, we obtain the solutions of the equation of fluctuation velocity after Fourier transformation.Under the condition of the the mean velocity gradient being small, they represent the picture of eddies, of whick the homogeneous turbulence(both isotropic and non-isotropic)of the final period is composed. By using the eddies of these types at different times, we may compose the steady turbulent field with the constant velocity gradient and this field may represent the turbulent field in the central part of the channel flow or pipe flow approximately.Then we may obtain the double velocity correlation function of this turbulent field, which involves both longitudinal correlation coeffict f(γ/λ) and the transversal correlation coefficientg(γ/λ).We compare theoretical coefficients with the experimental data of these coefficients at initial period and final period of isotropic homogeneous turbulence. And then we obtain the relation-ship bettyeen the turbulent double velocity correlation coefficient f(γ/λ) and the mean velocity gradient. Finally,we get the expressions of the keynolds stress and the eddy viscosity coefficient.