The internal losses in the tip clearance region strongly influence the compressor performance and its operational range. Previous research proved that passive wall treatments with circumferential grooves in axial compressors effectively increase the compressor stall margin. The vortex generated inside the circumferential grooves create a resistance to the flow that leaks in the tip clearance region of the compressor. However, most works found in the literature on circumferential grooves in axial compressors deal only with high-performance single-stage axial compressors. Therefore, there is a need to investigate and analyze the behavior of circumferential grooves in a multi-stage environment. In the present work, a passive wall treatment with circumferential grooves was implemented in a multi-stage axial compressor. Different configurations of circumferential grooves were created at the casing of the first and second rotor rows used in a four-stage axial flow compressor. Numerical simulations were performed to evaluate the influence of the circumferential grooves on the performance of a multi-stage axial compressor. The results obtained after the simulations for the different circumferential groove configurations were compared with the results obtained for the compressor without casing treatment (smooth wall) for different rotational speeds. Furthermore, the complete compressor map characteristics were simulated for the different casing treatment configurations, and the results were compared with the compressor characteristics of the smooth wall case. The passive wall treatment with circumferential grooves produced changes in the multi-stage axial compressor flow field, especially in the tip clearance region, improving the compressor stability mainly for part load speeds.