The present research investigates the effect of the location and the width of single shallow circumferential groove casing treatment on the flow field and the stability improvement of NASA Rotor 37 utilizing the help of computational fluid dynamics. At first, steady state simulation of Rotor37 was presented for smooth casing (without groove). Then, forty five various grooved casing were simulated and compared with the smooth casing. The results indicated that narrow grooves had slight effect on the adiabatic efficiency but as the width of the groove was increased, a decline in efficiency was observed. The investigation on the stall margin revealed that narrow grooves next to the leading edge could improve the stall margin by a reduction in the size of vortex breakdown zone. Medium-width grooves displayed an effective role in delaying the separation-produced by shock wave and boundary layer interaction-on the blade suction side near the casing. This type of grooves could improve the stall margin more than narrow grooves when located on the top of separation zone near the blade suction side. Wide grooves had negative effect on the stall margin and caused a significant drop in the efficiency and the total pressure ratio of the compressor.