This paper proposes a novel control scheme for minimizing the line loss of three-phase converters under unbalanced grid voltages. Most prior works focus on balancing phase currents or eliminating dc-link voltage ripples. However, they do not consider rms currents, so the efficiency may be lowered. In this paper, the optimal current reference is proposed to minimize sum of squares of rms currents in three lines. As a result of the proposed strategy, the efficiency of both converter itself and overall power system can be enhanced. Also, we calculate another optimal solution for removing active power ripples and verify that it coincides with previous works. Nevertheless, the corresponding control algorithm utilizes only line-to-line voltages, not positive- and negative-sequence ones; therefore, the proposed scheme does not include an extraction of sequential components and exhibits simpler implementation than its conventional counterpart. Experimental results prove the validity and the effectiveness of the proposed method.