The invention relates to a vehicle (1) including: - a towing axle (3) connected to a heat engine (5); - a directional axle (2); and - a complementary axle (4) that is neither directional nor motor-driven. When said vehicle is hybridized according to the method of the invention, the wheels of the complementary axle (4) are removed and replaced by in-wheel motors (12a, 12b), each connected with an inverter (13a, 13b) specifically dedicated for supplying electrical power thereto from an electrical power battery (14). A control housing (16) is also provided, that has built-in acceleration control means connected to the accelerator pedal (7), and built-in deceleration control means connected to the brake pedal (8), so as to control and monitor all the means needed for the driver to transparently accelerate and decelerate the vehicle.