A large-scale Wall-Resolved Large Eddy Simulation（WRLES）has been conducted for a transonic axial compressor rotor, NASA Rotor 37. By using a very fine computational grid of 1.35 billion points for a single passage and a high resolution scheme based on a 6th-order compact interpolation, the fine scale eddies in the turbulent boundary layer were resolved, and the interaction between the shock wave and the blade boundary layer, and the boundary layer separation due to the shock wave interaction were clearly captured. The WRLES results of the total pressure distribution at the rotor exit was in good agreement with the experimental results, and the pressure deficit on the hub side was well captured in the WRLES results. The total pressure on the shroud side was slightly overestimated in the WRLES results, which is due to an underestimation of the tip leakage vortex and its associated flow loss.