Analytical expression to calculate propagation constant and mode field of the hollow core Bragg fiber is derived. Numerical results are presented. It is shown that the fundamental mode of the hollow core Bragg fiber is circularly symmetric TE01 mode with no polarization degeneracy, while the higher order mode may be HE11, TM01, or TE02 etc.. This property is different from conventional optical fiber that its fundamental mode is the linearly polarized HE11 mode and is polarization degeneracy.