Internal cooling using ribbed cooling channels is considered as one effective method of cooling the gas turbine blades. The rib shape and arrangement can significantly affect the heat transfer and pressure drop in a channel, and there is always a trade-off between the thermal performance and friction along a ribbed cooling channel. This work aims to study the performance of circular and triangular rib shapes in comparison to the typical square rib shape in a cooling channel via the numerical solution of the Reynolds-averaged Navier-Stokes (RANS) equations benefiting from the computational fluid dynamics (CFD) methods. The present three-dimensional simulations are carried out in a square cross-section channel for the range of Reynolds number from 10,000 to 30,000 and constant heat fluxes at solid walls. The numerical solution of turbulent flow around the tested ribs is validated against the experimental data and is discussed. The results show that the circular rib would show a lower Nusselt number and lower pressure drop behavior compared to the square rib. On the other hand, the triangular rib enhances the Nusselt at the cost of the pressure drop increase. However, inspecting the present achieved Nusselt number and pressure drop quantities, it is concluded that the circular rib has a better overall performance among the investigated cases.