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Enantio-conversion with the help of electromagnetic fields is an essential issue due to the chirality-dependence of many chemical, biological, and pharmaceutical processes. Here, we propose a method for this issue based on a five-level double-$Δ$ model of chiral molecules. By utilizing the breaking of left-right symmetry in the two $Δ$-type sub-structures, we can establish the chiral-state-selective excitation with one chiral ground state being excited to an achiral excited state and the other one being undisturbed. In the meanwhile, the achiral excited state will relax to the two chiral ground states. The two effects simultaneously acting on the chiral mixtures can convert molecules of different chiralities to the ones of the same chirality, i.e., the enantio-conversion via optical pumping. With typical parameters in gas-phase experiments, we numerically show that highly efficient enantio-conversion can be achieved. Our method works in the appearance of decoherences and without the precise control of pulse-durations (pulse-areas) and/or pulse-shapes. These advantages offer it promising features in promoting the future exploring of enantio-conversion.