The invention discloses a heart valve stent and a heart valve prosthesis. The heart valve stent comprises a stent main body, which comprises mutually connected grid structure units, wherein the stentmain body is divided into an inflow channel, a transition section and an outflow channel in the axial direction, the inflow channel, the transition section and the outflow channel are connected in sequence, the stent further comprises a limiting structure connected with the stent main body, and the limiting structure is distributed on the outflow channel or the transition section in the circumferential direction, and is provided with a first projection part for limiting the stent from moving from the inflow channel to the outflow channel. According to the invention, the limiting structure is arranged on the outflow channel of the stent, so that the stent can be prevented from moving towards the outflow channel under the scouring of blood flow; the inflow channel of the stent is arranged toadapt to the shape of the native tissue, and the outer skirt edge is arranged in the circumferential direction of the outer side of the inflow channel at the position attached to the native tissue, so that perivalvular leakage can be effectively prevented while the valve is prevented from moving towards the inflow channel; and the size of the inflow channel of the stent can be small so as to effectively prevent atrioventricular block, and the size of the outflow channel can be small so as to reduce the compression on the aorta.