Based on the steady-state incompressible Navier-Stokes equations, a topology optimization strategy for fluid-solid coupling structure was proposed to maximize cooling efficiency. The physical model was established based on the active cooling system for scramjet configuration, and the Galerkin finite element method (FEM) was used to discretize the Navier-Stokes equations. Furthermore, combined with the rational approximation of material properties (RAMP) method, the globally convergent method of moving asymptotes (GCMMA) was used to solve the mathematical optimal model with different boundary conditions and objective functions. Numerical examples were provided to demonstrate the validity and effectiveness of the optimization strategy. The optimal flow passages of scramjet active cooling system under constraints are given successfully. Compared with the initial channel, the performance of the topological channel in reducing average temperature and flow loss is significantly improved, and the temperature of the construction is more uniform to avoid the occurrence of concentrated high temperature areas. In practical engineering application, the preliminary configuration obtained from the topology optimization can be parameterized to further improve the cooling performance of the channel.