On a channel of an implantable cardiac generator, a cardiac lead is replaced by a vagus nerve stimulation VNS lead. The control circuit controlling the stimulation circuit of this channel of the generator is configured to generate sequences of VNS neurostimulation bursts according to a specific profile, synchronized or not with the heart rate. The control circuit dynamically controls the initial load voltage of the reservoir capacitor so as to adjust to a constant target value the electrical charge delivered to the nerve by each stimulating pulse, from a pulse to the next one and from a burst to the next one. This improves the consistency of the physiological effects of neurostimulation despite significant variations that may occur in impedance at the electrode/vagus nerve interface.