A transcatheter atrio-ventricular valve prosthesis (1) for functional replacement of an atrio-ventricular heart valve in a connection channel ( 10), having a circumferential connection channel wall structure (25), between the atrial chamber (15) and the ventricular chamber (20) of a heart, comprising a radially expandable tubular body (30) to be disposed in the interior of the connection channel (10) and extending along an axis (35), and a valve (40) arranged within and attached to the tubular body (30), wherein the tubular body (30) is provided with an outer circumferential groove (45) which is open to the radial outside of the tubular body (30) and which defines a groove bottom (46), whereby the tubular body (30) is separated by the outer circumferential groove into first (31) and second (32) body sections, and wherein the tubular body (30) is provided with a first plurality of projections (50, 55) which extend from the first or second body section (31, 32) in an axial direction of the tubular body (30) and each of which has a free end (60, 65) arranged to overlap the outer circumferential groove (45), further comprising an elongate outer member (75) to be disposed at the exterior of the connection channel wall structure (25) at a level of the circumferential grove (45), wherein the outer member (75) can at least partially extend around the tubular body (30) with valve tissue of the connection channel wall structure (25) being correspondingly circumferentially arranged between the tubular body (30) and the outer member (75) and in such a radial distance (R5) to the axis (35) of the tubular body (30) that the valve tissue of the connection channel wall structure (25) can be radially forced into the outer circumferential groove (45) so as to be at least partially located radially below the projections (50, 55).
