The motivation to design a more efficient and compact aircraft engine leads to a continuous increase in overall pressure ratio and decrease in the stage number in compressors. Compared to the traditional multi-stage compressor, a single-stage ultra-high-pressure-ratio centrifugal compressor with a pressure ratio higher than 10.0 can significantly improve the engine’s power-to-weight ratio and fuel economy with a reduced structure complexity. Thus, it has great potential to be adopted in the compression system of advanced aero engines, such as turboshaft engines, in the future. However, the highly narrow Stable Flow Range (SFR) of ultra-high-pressure-ratio centrifugal compressors is a severe restriction for engineering applications. This research focuses on the aerodynamic performance of a ultra-high-pressure-ratio centrifugal compressor, and three-dimensional simulation is employed to investigate the effect of Self-Recirculating Casing Treatment (SRCT) on the performance and stability of the centrifugal compressor. Firstly, the parametric model of SRCT is established to investigate the effect of geometry parameters (rear slot distance and rear slot width) on the aerodynamic performance of the centrifugal compressor. It is concluded that SRCT improves the compressor’s SFR but deteriorates its efficiency. Also, a non-linear and non-monotone relationship exists between the SFR and rear slot distance or width. Then, the flow mechanism behind the effect of SRCT is explored in detail. By introducing the SRCT, an additional flow path is provided across the blade along the circumferential direction, and the behavior of the shock wave and tip leakage flow is significantly changed, resulting in the obviously different loading distribution along the streamwise direction. As a result, the mixing and flow separation loss are enhanced in the impeller flow passage to deteriorate the efficiency. On the other hand, the blockage effect caused by the mixing of slot recirculation and mainstream flow near the impeller inlet increases the axial velocity and reduces the incidence angle below the 90% spanwise section, which is considered to effectively stabilize the impeller flow field and enhance the stability.