In this paper, the vibration propagation characteristic is investigated for periodic composite pipeline with crack damage. A novel modified transfer matrix method (TMM) is developed to investigate transverse Band Gap structures (BGs) considering fluid structure interaction, and validated by frequency response function (FRF) for finite period. Field transfer matrix is developed for straight pipeline conveying fluid, and point transfer matrix is derived for circumferential cracks damage based on spring hinge model, which could estimate the equivalent rotational stiffness by local flexibility coefficient method. It’s demonstrated that the existence of small crack damage has negligible effect on BGs, while severe crack damage has significant influence on vibration propagation even it only exists in a single cell. Meanwhile, the difference of FRF between cracked and perfect pipeline provides new idea in diagnosing the crack status. The influence of crack damage on BGs is mainly attributed to the equivalent rotational stiffness. Location of crack damage could affect the stiffness ratio of composite pipeline, and result in the change of original BGs. This study enriches the theoretical TMM for pipeline systems vibration with crack damage, and provides some reference for the stability design of periodic pipeline structures.