The invention mixes and pre-extracts the mixed solution of acidic organic extractants such as P507, P204, C272, and naphthenic acid with magnesium bicarbonate and / or calcium bicarbonate solution and rare-earth solution. The rare-earth ions are extracted into the organic phase, then the loaded organic phase containing rare-earth ions are obtained through clarification, and can be used for the extract separation of the mixed rare-earth feed liquid. After a plurality of different levels of extraction, washing, stripping, single rare-earth compounds or rare-earth elements-containing enrichments can be obtained. The magnesium bicarbonate and/or calcium bicarbonate solution are prepared by roasting, digesting, carbonizing magnesite, limestone, calcite, dolomite and similar minerals, so that the content of impurities, such as silicon, iron, aluminum is lower. Ternary phase sediment is not produced in the pre-extraction and extraction separation process, so that the purity of the rare-earth products are not affected. The organic phase does not need ammonia saponification and does not produce ammonia-nitrogen wastewater. By adopting the invention, the production cost of rare-earth products is greatly lowered and the cost for three waste disposal is also greatly saved.