Abstract: It is very important of understanding the internal flow field in high speed centrifugal compressor in order to design an impeller with higher efficiency and high pressure ratio.In this paper,a three-dimensional viscous code has been developed to solve simplified Reynolds-averaged Navier-Stokes equations .The viscosity is simulated with viscous body force method.The governing equations are spatially discretized in the cell-vertex finite volume scheme on a simple H mesh and temporally integrated by an explicit two-step Runge-Kutta scheme.The turbulence closure is made by using Baldwin-Lomax model.This code is demonstrated for predicting the internal flow field of a high speed impeller.Some laser measure data are also illustrated to testify the calculated results.