A prosthetic heart valve includes an annular frame that has an inflow end and an outflow end and is radially compressible and expandable between a radially compressed configuration and a radially expanded configuration. The prosthetic heart valve further includes a leaflet structure positioned within the frame and secured thereto, and an outer sealing member mounted outside of the frame and adapted to seal against surrounding tissue when the prosthetic heart valve is implanted within a native heart valve annulus of a patient. The sealing member can include a mesh layer and pile layer comprising a plurality of pile yarns extending outwardly from the mesh layer.