The present invention relates to an intervertebral disc prosthesis comprising at least three pieces including an upper plate (1), a lower plate (2), and a movable core (3) at least in relation to a plate, wherein it also comprises two anatomic adaptation elements (11,22) of which each has, on one hand, a surface (110,220) in contact with a surface of a vertebra and, on the other hand, a surface (111) of which at least a part has a surface in contact with at least a part of the plate (1 or 2) opposite to which the anatomic adaptation element (11 or 22) is mounted, the anatomic adaptation elements (11,22) being fixed onto the plates (1,2) via fixation means (113,223). The prosthesis is fixed to the bone by an anchor (60) including a plate the end of which is folded over itself to be interlocked with the prosthesis.
