Using the Green function technique, the H-F ground state energy of the symmetric Anderson lattice is caolulated. Then the correlation energy, ground state energy, local moments, charge-and Spin-fluctuations of the correlation ground State are caclulated with the local approximation. Corresponding analytical formulas are obtained for a rectangular density of state. The result indicates that local moments decrease with decreasing value of the one-site f-f coulomb interaction U and or increasing value of the d-f hybridization strength V.