This paper proposes a current limits distribution control strategy for a parallel hybrid electric vehicle (parallel HEV) which includes an advanced powertrain concept with two electrical driving axles. One of the difficulties of an HEV powertrain with two electrical driving axles is the ability to distribute the electrical current of one high voltage battery appropriately to the two independent electrical motors. Depending on the vehicle driving condition (i.e., car maneuver) or the maximization of the entire efficiency chain of the system, a suitable control strategy is necessary. We propose an input-output feedback linearization strategy to cope with the nonlinear system subject to input constraints. This approach needs an external, state dependent saturation element, which translates the state dependent control input saturation to the new feedback linearizing input and therefore preserves the properties of the differential geometric framework. Numerous simulation studies are presented.