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We theoretically study the Casimir interaction between Weyl semimetals. When the distance a between semi-infinite Weyl semimetals is in the micrometer regime, the Casimir attraction can be enhanced by the chiral anomaly. The Casimir attraction depends sensitively on the relative orientations between the separations (b 1, b 2) of Weyl nodes in the Brillouin zone and show anisotropic behavior for the relative orientation of these separations (b 1, b 2) when they orient parallel to the interface. This anisotropy is quite larger than that in conventional birefringent materials. The Casimir force can be repulsive in the micrometer regime if the Weyl semimetal slabs are sufficiently thin and the direction of Weyl nodes separations (b 1, b 2) is perpendicular to the interface. The Casimir attraction between Weyl semimetal slabs decays slower than 1/a4 when the Weyl nodes separations b 1 and b 2 are both parallel to the interface. [ABSTRACT FROM AUTHOR]