This article conducts numerical investigation coupled with Reynolds-averaged Navier–Stokes method on detailed flow field and heat transfer characteristics of ribbed channel with symmetric ribs mounted on two walls. The physical domain is modeled by reference to a practical turbine blade internal cooling channel. The effects of three selected geometric factors of ribs, i.e., rib inclination angle, dimensionless rib height, and dimensionless rib pitch, on the flow and heat transfer are investigated by variable-controlled simulations with the Reynolds number ranges from 5000 to 90,000. The parameter ranges are 30 deg ≤ α ≤ 90 deg, 0.5 ≤ e/w ≤ 1.5, and 5 ≤ P/w ≤ 15 with the rib width w fixed at 1 mm. It is newly found that the friction factor does not follow a monotonical trend with respect to the Reynolds number under certain rib configurations. In addition, three-level numerical calculations about three geometric factors as well as the Reynolds number are conducted with the response surface method (RSM). Quadratic regression model for the targeted response, thermal performance factor (TPF), is obtained. The optimal rib shape for the goal of maximizing the channel overall thermal performance turns out to be e/w = 0.5, P/w = 15, and α = 30 deg as Re is fixed at 30,000.