The present invention relates to an intervertebral disc prosthesis preferably comprising at least three pieces including an upper plate (1), a lower plate (2) and a mobile core (3) at least in relation to the lower plate (2), co-operation means (23, 33) allowing to limit or eliminate the movements of the core (3) in relation to the lower plate (2), in translation and in rotation, respectively, about an axis substantially parallel to the lower plate (2) and about an axis substantially perpendicular to the lower plate (2), at least one part of the surface of at least one plate being concave and complementary with a convex surface (30) of the core (3), with which it is in contact, wherein the tip (31) of the convex surface (30) of the core (3) is off center, in at least one direction, in relation to the center (32) of this convex surface (30).