The characteristic impedance of the slab line with a circular conductor having an anisotropic dielectric is presented by rising the affine and conformal transformations. Moreover, a simpler approximate formula of the impedance expressed in term of epsilon /spl par/, epsilon /spl perp/, and r/h is also presented, where epsilon /spl par/, epsilon /spl perp/ r, and h, are the principal axes-relative dielectric constants of the anisotropic dielectric, the inner conductor radius, and the half Iength between ground planes, respectively.