This paper addresses the control design and the experimental validation of a current mode control for a three phase voltage source rectifier. The proposed control law is able to fulfill the voltage regulation and the current tracking control objectives despite of unbalanced and distorted grid voltages. The proposed control law consists of two loops, which are referred as inner tracking loop and the outer voltage regulation loop. The inner loop is designed to provide damping to the system, which also includes and adaptive mechanism. The construction of the current reference is based on the positive component detection of the grid voltage. Therefore, the current produced by the power rectifier is proportional to the fundamental component of the grid voltage, despite of the presence of unbalanced grid voltages. The voltage regulation loop is designed as a proportional-integral controller, which is aimed to regulate the DC output voltage to a desired level. Finally, experimental results are obtained in an experimental prototype of 2 kW to evaluate the performance of the proposed controller.