A high-birefringence holey fiber geometry is proposed, in which the cladding holes form a round lattice array. The birefringence properties are simulated by the finite difference beam propagation method. The influence of the cross-section structure parameters on birefringence is analyzed. The birefringence performances from round, quadrilateral and octagonal lattice arrays are compared. The results show that the modal birefringence of the holey fiber with round lattice can reach the order of 10-2 in 1.7~2.0 μm wavelength range. In the cross-section under the same structural parameters, the holey fiber with round lattice has a higher birefringence than those with quadrilateral and octagonal lattices. The polarization beat length is in sub-millimeter level in the 0.6~2.0 μm wavelength range. This fiber is suitable for making polarization interferometric fiber devices and sensors.