An annular barrier system for expanding an annular barrier in an annulus between a well tubular structure and an inside wall of a borehole downhole includes an annular barrier having a tubular part for mounting as part of the well tubular structure, the annular barrier further comprising an expandable sleeve surrounding the tubular part, at least one end of the expandable sleeve being fastened in a fastener of a connection part in the tubular part. The annular barrier system also comprises a tool for expanding the expandable sleeve by letting a pressurized fluid through a passage in the tubular part into a space between the expandable sleeve and the tubular part.