The non-uniform pressure generated in the volute generally are propagating upstream. As a result, outlet conditions of rotaing impeller are changed and the performance degrades. The major object of this research is to develop the numerical method which can calculate the effects of impeller and volute flow field interactions. Under the assumption of steady three-dimensional incompressible turbulent flow, the time averaged N-S equations involving $k-{epsilon}$ turbulent model was solved by the F.V.M. To verify the computational method, the calculations are compared with experimental results published in literature and show satisfactory agreement with them, The three-dimensional flow characteristics within the volute of a centrifugal fan at design and off-design operating points have also been studied.