The authors have recently proposed a novel degradative solvent extraction method that upgrades and fractionates various types of low-rank coals or biomass wastes into several different molecular weight fractions at around 350 degrees C. The lowest molecular weight fraction that was recovered as solid (termed soluble) by the yield of 19.4-71.7 wt % on a carbon basis had unique and almost raw-material-independent properties: almost free from ash and moisture, average molecular weight of around 300, carbon content of as high as 81.5-84.8 wt %, and oxygen content of as low as 6.5-12.1 wt %. In this work, the combination of the proposed extraction method and the liquefaction of the soluble under mild conditions was investigated as a two-stage liquefaction method to produce liquid fuel. A rice straw (RS) and a brown coal (LY) were extracted by the proposed extraction method to produce solubles by the yields of 31.5 and 21.7 wt %, respectively. The solubles produced were then liquefied at 400 degrees C using FeOOH/sulfur as the catalyst under the H-2 pressure of as low as 2.0 MPa (at room temperature). Then, 62.1 wt % of RS soluble and 56.8 wt % of LY soluble were converted to the liquid fraction (oil), excluding H2O. The oxygen contents of the oils produced from the two-stage liquefactions of RS and LY were as low as 2.2 and 3.9 wt %, respectively, much lower than those from the direct liquefaction of the raw materials (single-stage liquefaction). Furthermore, both the amount of CO2 emitted and the amount of H-2 consumed during the two-stage liquefaction were much less than those of the single-stage liquefaction. Thus, it was shown that combining the degradative solvent extraction method and the liquefaction of the soluble is a promising method to produce high-quality liquid fuel from low-rank coals and/or biomass wastes.