A prosthetic valve assembly for use in replacing a deficient native valve comprises a replacement valve supported on an expandable valve support. If desired, one or more anchor may be used. The valve support, which entirely supports the valve annulus, valve leaflets, and valve commissure points, is configured to be collapsible for transluminal delivery and expandable to contact the anatomical annulus of the native valve when the assembly is properly positioned. The anchor engages the lumen wall when expanded and prevents substantial migration of the valve assembly when positioned in place. The prosthetic valve assembly is compressible about a catheter, and restrained from expanding by an outer sheath. The catheter may be inserted inside a lumen within the body, such as the femoral artery, and delivered to a desired location, such as the heart. When the outer sheath is retracted, the prosthetic valve assembly expands to an expanded position such that the valve and valve support expand within the deficient native valve, and the anchor engages the lumen wall.