3-D Navier-Stokes codes with the k-ε turbulence model and the wall function have been widely used for the flow simulation in turbomachinery with a high Reynolds number. Two centrifugal pumps of low specific speeds with vaneless diffusers were used in this study. The blade shape of these impellers is characterized by the large thickness at the outlet and results in the difficulty of grid generation on the computational model. In order to demonstrate the effects of the grid generation and boundary condition between stationary and rotational parts to the simulation results, some computational models are studied using the 3-D Navier-Stokes code. These simulation results are finally compared with experiments and the applicability of the Navier-Stokes code will be discussed.