A ventricular assist assembly, for assisting a heart,includes an anchoring device, a cardiac pump and a stabilizing device. The anchoring device anchors a cardiac pump, is intended to be assembled with an opening in a ventricular wall of the heart, and delimits an internal passage.The cardiac pump is intended to be attached to the anchoring device, is configured for intra-ventricular insertion into the heart, and has a distal end.The cardiac pump extends through the internal passage into the heart when attached to the anchoring device implanted in the opening so that its distal end is placed in a ventricular chamber.The stabilizing device stabilizes the cardiac and includes at least two elongate, biocompatible and flexible connecting members, each elongate connecting member being intended to connect a part of the cardiac pump that is positioned in the ventricular chamber to an internal wall of the ventricular chamber.