The present study is conducted to investigate the effect of rib arrangements on an impingement/effusion cooling system with initial crossflow. To simulate the impingement/effusion cooling system, two perforated plates are placed in parallel and staggered arrangements with a gap distance of 2 times of tile hole diameter. Initial crossflow passes between the injection and effusion plates, and the square ribs (3mm) are installed on the effusion plate. Both the injection and effusion hole diameters are 10mmand Reynolds number based on the hole diameter and hole-to-hole pitch are fixed to 10,000 and 6 times of the hole diameter, respectively. To investigate the effects of rib arrangements, various rib arrangements, such as 90$^{circ}$transverse and 45$^{circ}$angled rib arrangements, are used. Also, the effects of flow rate ratio of crossflow to impinging jets are investigated. With the initial crossflow, locally low transfer regions are formed because the wall jets are swept away, and level of heat transfer rate get decreased with increasing flow rate of crossflow. When the ribs are installed on the effusion plate, the local distributions of heat/mass transfer coefficients around the effusion holes are changed. The local heat/mass transfer around the stagnation regions and the effusion holes are affected by the rib positions, angle of attack and rib spacing. For low blowing ratio, the ribs have adverse effects on heat/mass transfer, but for higher blowing ratios, higher and more uniform heat transfer coefficient distributions are obtained than the case without ribs because the ribs prevent the wall jets from being swept away by the crossflow and increase local turbulence of the flow near the surface. Average heat transfer coefficients with rib turbulators are approximately 10% higher than that without ribs, and the higher values are obtained with small pitch of ribs. However, the attack angle of the rib has little influence on the average heat/mass transfer.