The van der Waals interaction of a pair of anisotropic molecules near planar dielectric surfaces is studied by using the linear response formalism. The spatial correlation function (Green function) of the vacuum electric field in the presence of dielectric surfaces is obtained by using suitable Fresnel mode functions of the quantized electric field. In the short-distance limit, it is observed that the long-range interaction potential is significantly modified by the dielectric surfaces and strongly depends on the geometry of the two molecules near dielectric surfaces. When the two molecules are anisotropic, depending on the molecular alignments with respect to the surfaces, the van der Waals interaction is enhanced or suppressed by the existence of the surfaces. When the two molecules are in between two dielectric surfaces, the overall magnitude of the van der Waals interaction is suppressed in comparison to that in the free space because the vacuum electromagnetic field intensity is reduced by the transmissivities that are generally less than unity.