Sensorless control theory is considered as one of the most important keys to reduce the cost of manufacturing and maintenance in automotive applications. This article presents a current sensorless control algorithm of a wound rotor synchronous machine using a model-free-adaptive control (MFAC). The only controlled variable in this method is the rotor speed, and no observation or estimation will be performed on the phase currents. The presented controller is also compared with a current sensorless control method that uses a Lyapunov-based observation of phase currents in the control algorithm. The developed control algorithm is first tested in simulation under several operating conditions, such as starting, tracking, parameter variation, and load step. Then, experimental tests validated the effective performance of MFAC in a current sensorless control algorithm. According to these results, the control of phase currents is guaranteed with a small error but without using any current sensors.