Electrical grid modernization concept promotes the use of DC subgrids in order to improve efficiency, minimizing energy conversion count in the source-to-load chain. The present paper discusses an average current sensorless control algorithm for proposed bidirectional AC/DC converter, which is based on a dual half-bridge topology with common neutral wire that is not commutating during converter operation. The proposed current sensorless control algorithm has been obtained analytically for rectification, grid-tied and stand-alone inverter modes. The average value of inductor current tracks the reference current signal with constant switching frequency. Two control functions for inductor’s discontinuous and continuous current modes have been defined for each of the operation modes, and a sensorless transition between DCM and CCM modes has been stated. The proposed sensorless control algorithm has been also adapted for use with LCL input filter. The results of simulation in the PSIM software approved the analytical model, keeping the average inductor current to follow the reference value in inductor discontinuous and continuous conduction modes. Experimental investigation of the proposed current control algorithm provided similar results confirming the discussed theory.