For any practically applied AC/DC hybrid distribution network (AC/DC-HDN), the hard issue of removing DC short-circuit currents must be solved by a cost-effective scheme. However, up to now, in the most published achievements of AC/DC-HDN, the systematic scheme to address the above issue is rarely found. This paper proposes a novel strategy with a low cost for solving this problem. The proposed strategy can: (i) greatly decrease the DC short-circuit current components flowing from the AC/DC converters to the fault point, (ii) fast switch off the paths of DC short-circuit current components from DG branches to the fault point, (iii) completely block the DC short-circuit current components that feed into the fault point from the capacitors paralleled on the DC ports of load branches. Also, in this paper, a new topology of DC/DC converter with a controlled zero-current output function is proposed for fast switching off the paths of DC short-circuit current components from DG branches to the fault point. The scheme of relay protection and automatic control matching with the proposed strategy is designed. The principles of the scheme and design are explained in detail. The simulation results verified the effectiveness of the proposed strategy are given.