The present invention relates to an annular barrier to be expanded in an annulus between a well tubular structure and an inside wall of a borehole downhole. The annular barrier comprises a tubular part for mounting as part of the well tubular structure, an expandable sleeve surrounding the tubular part and having an inner face facing the tubular part, each end of the expandable sleeve being connected with a connection part which is connected with the tubular part, a space between the inner face of the sleeve and the tubular part, and an element arranged in connection with the sleeve, the element having a first part and a second part both of which extend around the inner face, the first part of the element being fastened to the inner face.