Angled ribs have been widely used in the rectangular internal cooling channel of gas turbine to enhance heat convection strength and the optimal rib parameters have been shown in the former investigations. However, the heat transfer strength of the wall near the terminal of angled ribs is less enhanced by the rib and the local Nusselt number ratio may be lower than 1, which means that the local heat transfer strength of the ribbed wall is lower than that of smooth wall. At the same time, the ribs also generate large friction loss. As a result, a part of ribs which provides little heat transfer enhancement effect are removed in order to both reduce friction loss and maintain or enhance local heat transfer strength. In order to find out the optimal geometry parameters of the removed part of the rib, the optimization study are conducted in this paper based on the ANSYS Workbench software. The channel width to height ratio is 1 and 4. The rib attack angle is 45 degrees. The length of removed part, the transverse location of the removed part and the angle between the flow direction and the incision edge are chosen as the design variables. The area-averaged Nusselt number ratio and temperature on the ribbed wall, the friction factor ratio of the channel and the thermal performance factor are chosen as the objectives. The samples are generated by Latin Hypercube Sampling method and the CFD calculation is conducted by ANSYS CFX module using SST turbulence model. The response surface is obtained by Kriging model based on the CFD results and the Pareto optimal solution of this multi-objective problem is conducted by Multi-Objective Genetic Algorithm (MOGA) in the Response Surface Optimization module of ANSYS Workbench. The results show that the removed part of rib could both maintain or slightly enhance the overall Nusselt number ratio and obviously reduce the friction factor at the same time. Furthermore, the Nusselt number ratio in the terminal region of original ribs is also largely enhanced.