Casing treatment is an efficient technique which is used to increase the compressor stall margin with a minor reduction in the efficiency. The interaction between the blade passage and the groove is the main cause of the stall margin improvement by various researches. A numerical study is conducted on a single circumferential casing groove using NASA rotor 37 in the current study. The performance of the two circumferential groove models is studied by discretizing RANS 3D equations using a finite volume technique. The inception of the stall is predicted according to the criteria of convergence. Two models of the circumferential groove have been suggested and numerically tested. A single passage simulation is selected for the two models. The performance of the smooth casing and the two models are analyzed. Moreover, the stall margin, total pressure ratio and peak adiabatic efficiency of the normal casing, and the two models are analyzed to determine the influence of the groove on the axial compressor performance and stability. Models 1 and 2 stall margins are enhanced by 6.62 % and 4.45% respectively. The adiabatic efficiency of model 1 and model 2 are decreased by 0.79 % and 1.08 % respectively.