A cover structure is disclosed. When an annular sealing portion of a cover body is engaged with a container, a sealing section of the annular sealing portion abuts against an annular inner surface of the container, and then, a folding section of the annular sealing portion is folded to a sealing state, so that part of the folding section abuts against the annular outer surface of the container to form a dual leak-proof sealing structure. The folding section of the annular sealing portion is an annular elastic and full-peripheral tightening structure. Therefore, the sealing between the container and the cover may be strengthened for a good sealing effect, and preventing liquid in the container from being splashed on surrounding articles. When the folding section is in the unsealing state, the cover can be separated from the container, which is convenient to carry and use.