A transcatheter valve prosthesis includes an expandable tubular stent, a prosthetic valve within the stent, and an anti-paravalvular leakage component coupled to and encircling the stent which includes a plurality of self-expanding struts and an annular sealing membrane. Each strut has a first end coupled to a distal end of the stent and a second end not coupled to the stent. Each anti-paravalvular leakage component is moveable between a compressed configuration and a deployed configuration. In the compressed configuration, each strut extends distally away from the distal end of the stent. In the deployed configuration, each strut extends proximally away from the distal end of the stent. In an embodiment hereof, the deployed strut has a C-shape and is twisted such that the C-shape lies in a plane substantially along or tangential with the outer surface of the stent. In another embodiment hereof, the deployed strut is rolled-up and extends radially away from the outer surface of the stent.