Impeller is a very important element in rotating devices to deliver energy to/from the fluid. The diffusers are essential for effective transformation of the kinetic power produced by the rotor in a centrifugal fan. Hence the flow in the impeller and diffuser passages is the important phenomenon in optimizing the performance. These impeller and diffuser flow passages are the most complex regions to predict the flow behavior. With the advanced development of Particle Image Velocimetry as well as convenient numerical CFD tools, it has become possible to reach at an accurate result well-matched with the real behavior of the flow. Hence, in this work moving mesh technique is used to get a numerical solution for the estimation of actual flow manner. Numerous research works have been done recently to get the physics of fluid flow through impeller and diffuser, both numerically and experimentally. But it is found from the literature that the study on the performance of the fan by changing the number of impeller and diffuser blades together in a combination has not been the emphasis of attention in these works. Hence a numerical analysis has been carried out in this paper to comprehensively lookout the fluid interaction in impeller-diffuser as well as to envisage the flow behavior of the fan by changing the number of impeller and diffuser blades together in combination. For the same number of impeller blades, it is found from the analysis that a higher static pressure rise coefficient is achieved at the outlet of the fan for smaller number of diffuser blades. It is also found that larger the number of impeller blades, larger is the static pressure rise coefficient for the same number of diffuser blades, hence performance gets improved.