A numerical study was conducted on the multiple jet impingement heat transfer of the double-wall cooling with high blockage ratio ribs of various configurations. Three different blockage ratios (BR = 0.2, 0.3, and 0.5) and two rib arrangements relative to the effusion holes (l/Sx = 0.25 and 0.75) were thoroughly examined using the RANS method with the SST–KIC turbulence model, considering the Kato–Launder modification (K), intermittency (I), and crossflow (C) transition effects. The ratio of jet-to-target plate spacing to jet diameter (H/d) was fixed to be 1, and Reynolds numbers varied in the range of 4000–16,000. Furthermore, the computed data on the rib roughed wall were also compared with those on a flat plate for the double-wall cooling. The results demonstrate that the installation of the high blockage ribs significantly decreases the detrimental crossflow effect due to the blockage effect of the ribs and intensively disturbs the jet flow in flow passing over the ribs, thereby enhancing the heat transfer performance. For the impingement/effusion cooling, the arrangement of the rib downstream of the effusion holes (l/Sx = 0.25) shows more advantages, and the heat transfer level rises quickly as BR increases. The best thermal-hydraulic performance and heat transfer uniformity on the rib roughed target plate is both obtained at BR = 0.3, which can be increased by up to 10% and 8%, respectively, compared to those on the flat plate.