A bicycle clamp structure comprises a first clamp member, a second clamp member, a connecting member, a first connecting structure, a second connecting structure, and a third connecting structure. The second clamp member is configured to clamp a bicycle tube member between the first clamp member and the second clamp member. The connecting member is configured to be arranged between the first clamp member and the second clamp member. The first connecting structure is configured to connect the first clamp member with the connecting member. The second connecting structure is configured to connect the second clamp member with the connecting member. The third connecting structure is configured to connect the first clamp member with the second clamp member.