In this study, for a bellows expansion joint only subjected to axial cyclic displacement, the fatigue life is evaluated in accordance with the relevant standards for bellows expansion joints, and a numerical simulation of crack propagation for the fatigue life in case of a small crack existed on the bellows expansion joint is conducted based on fracture mechanics. Results indicate that based on the semi-elliptical surface crack model proposed herein, both the stress intensity factor at the crack front and the depth of crack propagation exhibit a rapid increase with an increasing number of cycles. Furthermore, it is observed that the propagation of the crack in the span direction exceeds that in the depth direction, leading the crack become more and more flat. For the bellows expansion joint and loads studied here, the fatigue life of the un-cracked corrugated expansion joint based on the standard is larger than that predicted by fracture mechanics for the corrugated expansion joint with a small crack by approximately 46%, which means the that the fatigue life calculated according to the standard of the bellows expansion joints could be over-estimated, and design this way cannot guarantee that the bellows expansion joint will not fail due to cracking.