A new surface shape of an internal cooling passage which largely reduces the pressure drop and enhances the surface heat transfer is proposed in the present study. The surface shape of the cooling passage is consisted of the concave dimple and the riblet inside the dimple which is protruded along the stream-wise direction. Direct Numerical Simulation (DNS) for the fully developed turbulent flow and thermal fields in the cooling passage is conducted. The numerical simulations for five different surface shapes are conducted at the Reynolds number of 2800 based on the mean bulk velocity and channel height and Prandtl number of 0.71. The driving pressure gradient is adjusted to keep a constant mass flow rate in the x direction. The thermoaerodynamic performance for five different cases used in the present study was assessed in terms of the drag, Nusselt number, Fanning friction factor, volume and area goodness factor in the cooling passage. The value of maximum ratio of drag reduction is -22.86 %, and the value of maximum ratio of Nusselt number augmentation is 7.05% when the riblet angle is $60^{circ}$. The remarkable point is that the ratio of Nusselt number augmentation has the positive value for the surface shapes which have over $45^{circ}$ of the riblet angle. The maximum volume and area goodness factors are obtained when the riblet angle is $60^{circ}$.