Insertion of multiple quantum wells (MQWs) into the i-region of GaAs p-i-n solar cells can shift the effective bandgap to the optimal value for single-junction solar cells under high sunlight concentration. The quantum efficiency corresponding to the absorption by MQWs must be sufficiently high for achieving high-efficiency single-junction MQW solar cells. Here, we report light-trapping thin-film MQW solar cells for increasing photoabsorption in MQWs. In order to suppress the free-carrier absorption loss and enhance the light trapping, only the active layers including MQWs were processed to a cell by flip-chip bonding and dissolution of a conductive GaAs substrate. The periodic grooves formed on the back side of the cell scattered photons in the subbandgap range and trapped light inside the cell. For absorption loss reduction in a back contact metal, a dielectric interlayer was introduced between the metal and GaAs. The light-trapping structure resulted in a fivefold increase in effective optical path length compared with the physical thickness of MQWs. External quantum efficiency at wavelengths longer than the GaAs edge exceeded 50% with only 20-period MQWs. As a result, we achieved thin-film light-trapping MQW solar cells with 20% conversion efficiency.