Abstract: Arbitrary Lagrangian-Eulerian schemes are deduced for computation of three dimensional viscous flow in rotating impeller channel.The convection effect is simulated by the pseudo-moving of grids.Viscous sub-cycle time step and Lagrangian sub-cycle time step are adopted to accelerate convergence.The upwind scheme is improved into part-donated scheme to diminish diffusion. Flowrate restriction is used to control dissipitive truncation error.A short wave damp is introduced to reduce the computational corrugation.Sub-Grid-Scale(SGS) turbulent model is adopted to simulate turbulent flow.Eckardt's experimental results on centrifugal impeller have verified effectiveness of the method.