This study was carried out to investigate the high-acidity co-separation of Am and RE from a simulated radwaste solution by a solvent extraction using a mixture of Dimethyldibutyltetradecylmalonamide (DMDBTDMA, as an extractant) and dihexyl octanamide (DHOA, as a phase modifier) diluted with n-dodecane (NDD). All the experiments were conducted as a batch type. First, the environmentally friendly DMDBTDMA and DHOA composed of only CHON atoms were self-synthesized. Then, the conditions for the prevention of a third phase, generated in the organic phase were examined. In addition, the effects of the concentration of nitric acid, DHOA, oxalic acid and $H_2O_2$ on the co-extraction of Am and RE were elucidated. Consequently, the optimum condition of (0.5M DMDBTDMA+0.5M DHOA)/NDD-0.3M $C_2H_2O_4-4.5M$ $HNO_3$ and O/A=2 was obtained through experimental work. Under this condition, the extraction yields were found to be about 80% for Am, more than 70% for RE such as La, Eu, Nd, Ce, etc., 3% for Cs and Sr, 69% for Fe and less than 11% for Mo and Ru. For the co-extraction of Am and RE, Fe should be removed in advance or prevented from a co-extraction with Am by controlling the different extraction rates of Am and Fe. About 95% of the Am and RE in the organic phase were stripped using a 0.5M $HNO_3$.