In turbine engines, ribbed channels are a common internal cooling structure that can significantly enhance heat transfer but often lead to a noticeable reduction in flow performance. Although many optimization methods have been proposed to address the issue, it is challenging to improve both flow and heat transfer performance. In the present study, a cross-scale design concept that combines both micro-ribs and macro-ribs is proposed to optimize both flow and heat transfer performance simultaneously. Using the v2f turbulence model, the feasibility of this new design is evaluated through comprehensive three-dimensional numerical simulations across a wide range of Reynolds numbers from 20 000 to 80 000. For the macro-ribs, the linearly decreasing height (LDH) rib arrangement with the best heat transfer performance in existing studies is used. For the micro-ribs, different designs are tested, including blade ribs, triangular ribs (sawtooth ribs), and trapezoidal grooves (interval triangular ribs). The simulation results demonstrate that the combination of micro-ribs and macro-ribs can not only enhance heat transfer performance but also significantly reduce pressure loss. The improvement is attributed to the micro-ribs increasing the gas flow velocity near the wall. This not only reduces flow resistance but also enhances heat exchange between the main gas stream and the wall. Among the three kinds of micro-ribs, blade micro-ribs with the highest shear stress reduction rate have the greatest improvement on the overall thermal performance of LDH rib channels. Specifically, the factor (Nu/Nu(0))/(f/f(0)) increased by 8.06%, and the factor (Nu/Nu(0))/(f/f(0))(1/3) increased by 3.24%.