The improved point-matching method with Mathieu function expansion for the accurate analysis of the W-type elliptical fiber with layers of any ellipticity is proposed. Results of our method are reliable, because we expand the electromagnetic fields by a sum of the complete set of wave functions in each layer of the fiber. Numerical results are presented for the highly-birefringent fibers with a hollow layer outside an elliptical core. It is found that such fibers can realize the large value of the modal birefringence as well as they can be suitable for the single-mode and single-polarization transmission. From the convergence tests, it is confirmed that the relative error of the modal birefringence is less than 0.01%. The comparison of our results with those by previously reported method is presented. The proposed method can be extended for analysis of the elliptical-core fibers with hollow pits and electromagnetic scattering by targets of the complex elliptical geometry.