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We utilize variational method to study the Kondo screening of an Anderson impurity in three-dimensional Dirac and Weyl semimetals.We find that the spin correlation between the magnetic impurity and conduction electrons in both the systems are strongly anisotropic due to the spin-orbit coupling,and the spin-spin correlations are of power-law decay in both systems.The differences between Dirac and Weyl semimetals are also investigated.