As the demand for high-pressure-ratio and high-flow-rate centrifugal compressors increases, aerodynamic noise has become a key factor constraining their development. This paper investigates the effects of tip clearance on compressor performance and aerodynamic noise at near-stall conditions through numerical calculations and experiments. Firstly, the numerical model of the centrifugal compressor with original tip clearance was established. Then, the compressor’s aerodynamic performance and aerodynamic noise were calculated using the high-precision computational fluid dynamics (CFD) approach and the boundary element method (BEM), and the numerical results were validated against experimental data. Finally, the effects of non-uniform tip clearance on compressor performance and aerodynamic noise were analyzed. The results show that reducing the leading and trailing edge tip clearances improves the compressor’s aerodynamic performance compared to uniform tip clearance, and reducing the trailing edge clearance has a greater effect. Under near-stall conditions, increasing or decreasing tip clearances can somewhat reduce aerodynamic noise compared to uniform tip clearance. The aerodynamic noise is less sensitive to non-uniform tip clearance changes when tip clearance is reduced. However, when tip clearance is increased, smaller non-uniform trailing edge clearances significantly reduce aerodynamic noise.