Voltage sensing in a three-phase grid-connected inverter can be expensive, and introduces vulnerability to the sensor's failure. To address this problem, a sensorless current control strategy is introduced which is composed of two basic elements. First, a current controller based on a Lyapunov energy function is derived by the assumption of known grid voltage. Next, a dual second-order generalized integrator (DSOGI) structure is utilized to extract the positive sequence grid voltage from the Lyapunov-based current controller outputs and generate the unit vectors from the phase locked loop. The methodology presented has been verified in simulation using MATLAB/Simulink and PLECS. Experimental validation is provided by a reduced scale laboratory prototype.