The self-circulating casing treatment can effectively expand the stable working range of the compressor, with little impact on its efficiency. With a single-stage transonic axial flow compressor NASA (National Aeronautics and Space Administration) Stage 35 as the research object, a multi-channel unsteady numerical calculation method was used here to design three types of self-circulating casing treatment structures: 20% Ca (axial chord length of the rotor blade tip), 60% Ca, and 178% Ca (at this time, the bleed position is at the stator channel casing) from the leading edge of the blade tip. The effects of these three bleed positions on the self-circulating stability expansion effect and compressor performance were studied separately. The calculation results indicate that the further the bleed position is from the leading edge of the blade tip, the weaker the expansion ability of the self-circulating casing treatment, and the greater the negative impact on the peak efficiency and design point efficiency of the compressor. This is because the air inlet of the self-circulating casing with an air intake position of 20% Ca is located directly above the core area of the rotor blade top blockage, which can more effectively extract low-energy fluid from the blockage area. Compared to the other two bleed positions, it has the greatest inhibitory effect on the leakage vortex in the rotor blade tip gap and has the strongest ability to improve the blockage at the rotor blade tip. Therefore, 20% Ca from the leading edge of the blade tip has the strongest stability expansion ability, achieving a stall margin improvement of 11.28%.