We study the complex ac admittance tensor (ac conductivity and dielectric constant) of anisotropic conductor-insulator composite materials, based on anisotropic two-dimensional RC-networks consisting of randomly placed conductors and capacitors with different conductor existence (bond occupation) probabilities in two directions. We calculate numerically each component of the complex ac admittance tensor by applying a transfer matrix method and reveal the effect of the anisotropy of the bond occupation probability on the frequency characteristics of the ac admittance tensor. It is found that the dual relation holds for each diagonal component of the complex admittance tensor of the anisotropic two-dimensional RC-network. For the effective conductance in the metallic region, the anisotropy depends not only on the anisotropy of the bond occupation probability, but also on the frequency omega. We derive the analytical relation between the anisotropy of the conductance and the anisotropy of the bond occupation probability, at both the dc limit and omega RC = 1. The calculated results on the ac admittance are compared with the effective medium theory and how the accuracy of the theory is related with the microscopic current path is clarified.