This paper presents a study on the performance of NASA Rotor 37 with the casing grooves based on three-dimensional numerical analysis. Reynolds-averaged Navier-Stokes equations are solved on a hexahedral grid with the shear stress transport model as a turbulence closure model. The governing equations are discretized by a finite volume method. The validation of the numerical results is performed through experimental data for the total pressure ratio and the adiabatic efficiency. The investigation for an axial compressor with a smooth casing and the casing grooves is carried out to compare the performance parameters, for example, surge margin and efficiency, etc. The surge margin is improved in the case of the casing grooves while remarkable improvement of the efficiency is not produced. The result shows that the casing groove is beneficial to expand the operating range of NASA Rotor 37.