Abstract: In view of the oscillation problem that easily occurs during the numerical solution of the compressible Navier–Stokes (N–S) equations at high Reynolds (Re) numbers, this paper constructs a high–order Compact Central Weighted Essentially Non–Oscillatory(CCWENO) type entropy–stable scheme. In the spatial direction, this scheme combines the high – order entropy – conservative flux with the CCWENO – type reconstruction of the entropy variable in the dissipation term to construct the high – order entropy – stable flux. For the heat flux term and the viscous term, a central scheme is adopted for discretization to achieve a low – dissipation effect, thus constructing the high–order numerical flux. Using the method of dimension–by–dimension extension, the scheme was successfully extended to the multi–dimensional case, and it was proven that the reconstructed high–order numerical scheme satisfies the entropy stability property. The good performance of the algorithm is verified through several numerical examples. The numerical results show that this scheme can accurately capture discontinuities, has high resolution and strong numerical stability for the N–S equations at high Re numbers.