Based on the four-level double-model composed of two degenerated (left-and right-handed) chiral ground states and two achiral excited states, we propose a purely coherent-operation method for enantioconversion of chiral mixtures. By choosing appropriate parameters, the original four-level model will be simplified to two effective two-level subsystems with each of them involving one chiral ground state. Then, with the help of welldesigned coherent operations, the initial unwanted and wanted chiral ground states are converted, respectively, to the wanted chiral ground state and an auxiliary chiral excited state with the wanted chirality, i.e., achieving the enantioconversion of chiral mixtures. Comparing with the original works of enantioconversion based on the four-level double-model with the requirement of the time-consuming relaxation step and repeated operations, our method can be three orders of magnitude faster since we use only purely coherent operations. Thus our method offers a promising candidate for fast enantioconversion of chiral molecules with short enantiomeric lifetime or in the experimental conditions where the operation time is limited.