It is well known that drag reduction occurs when the flow is passing by a grooved circular cylinder at certain Reynolds numbers, which has been used as a powerful energy saving method in a broad range of circumstances. However, a challenge here is how to evaluate the combined effects of depth, width and location of a given triangular groove set covering half of the cylindrical surface area. A useful approach to quantitatively analyze the influence of these different factors on drag reduction using the response surface methodology is described here. The flow characteristics, including drag coefficient, flow velocity, turbulent kinetic energy and vorticity, were calculated by numerical simulation. The results showed a great drag reduction effect under the legitimate set of groove structure parameters at a super-critical Reynolds number providing a base for optimization process in various engineering applications. The drag reduction mechanism found from this research could extend to other cases and should provide insights into engineering applications like car grilles.