In this paper,it is investigated the polarization and the dispersive properties of the elliptical highindex-core Bragg fibers via a powerful full-vector finite element method. The simulation results show that the modal birefringence of the elliptical high-index-core Bragg fibers is on the magnitude of 10^-3,about one order magnitude larger than that of conventional polarization maintaining fibers. The dependence of the modal birefringence on the fiber structural parameters has been fully investigated. The modal birefringence decreases with the filling ratio of the low-refractive-index material and changes little with the variation of the period of the cladding layers. Larger ellipticity or higher index-contrast will result in enhanced modal birefringence. These results will be helpful to the design of high performance one-dimensional microstructured polarization maintaining fibers.