Advanced aero-engines with higher flying Mach number, like SCRamjets, offer good solution to the hypersonic propulsion. However, the thermal boundary condition of the engine cooling channels is normally non-uniform, which may cause fuel mal-distribution. Serious fuel cooling capacity waste and even over-temperature may occur. To ensure the reasonable flow distribution and wall temperature, a parametric study of the cooling channel geometries is conducted under non-uniform thermal boundary condition. A 3D numerical model considering the flow and heat transfer under supercritical pressure in parallel cooling channels is developed and validated. The results indicate that the flow distribution and cooling effect both improve with the reasonable design of the channel geometry. Higher aspect ratio (AR) improves the flow distribution and cooling effect. The variations of rib thickness and total channel flow area show greater impact on the heat transfer performance than on the flow distribution. At last, the results of channel geometry optimization are validated under different heat flux distributions. It can be concluded that the channel geometry optimization in this work improves the flow distribution and lowers the wall temperature, which provides reference for the design of cooling channels in aero-engines like SCRamjets. (C) 2018 Elsevier Ltd. All rights reserved.