During the fabrication process of hollow-core Bragg fibers, outer diameter variations would be induced unavoidably, which lead to band gap shifts of the one dimensional photonic crystal structures in the fiber claddings, impacting their transmission characteristics severely. The mode transmission characteristics of hollow-core Bragg fibers with slowly sine variation in outer diameter have been investigated. The simulation results show that, despite the transmission characteristics are different between different mode classes and the mode losses are different between modes in the same mode class with different orders, the diameter variation tolerances are almost the same. In the case calculated, the diameter variation tolerances of the TE0n mode are about 9%, and 6%～7% for the TM0n, HE and EH modes. The method deployed can be used for any diameter variations and structure parameters.