In this paper, the edge-based finite element formula for calculating the dispersion characteristics of transmission lines loaded with anisotropic left handed materials and anisotropic right handed materials with electric field as working variable is derived, and the calculation is carried out by taking unilateral finline, bilateral finline and antipodal overlapping finline as examples. Firstly, the dispersion characteristics of three modes in three kinds of finlines are compared when the relative dielectric constant and permeability are fixed; Secondly, taking the unilateral fin line as an example, the changes of dispersion characteristics with the changes of relative dielectric constant and relative permeability in each direction are calculated. The calculation method and results derived in this paper further expand the application of anisotropic left handed and right handed materials in transmission lines, and also have great guiding significance for the use of finlines in microwave devices such as mixers, filters and resonators.