Numerical investigation of a centrifugal compressor volute having a modified straight conical duct hill been made. Three-dimensional Reynolds-Averaged Navier-Stokes equations with $k-{varepsilon}$ turbulence equation are solved To avoid coordinate singularity at the central axis of the duct, multi-block H-type grid is generated on the circular cross-sections of the volute and stretched toward the solid wall boundary. We obtained numerical results with three different mass flow rates at the volute inlet, namely, with the inlet conditions that give small, medium and large mass flow rates at the outlet of the conical duct. Agreement with the experimental results is observed.