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To solve the problem of rotor-stator flow coupling, the FVM was adopted to discretize the incompressible rotating flow equations. The time and spatial discretization schemes of the convective, diffusive, and the source term of the equations were investigated. For the rotor, the non-inertial reference frame was adopted to solve the relative flow equations, and for the stator, the inertial reference frame was adopted to solve the absolute flow equations. To keep flux conservation, the Neuman condition was prescribed on the rotor-stator interface. To realize the rotor-stator flow coupling, the relative velocity at rotor outlet was transformed to the absolute velocity, which used as the stator inlet condition. Then a switch mode was adopted to run the algorithm. To validate this algorithm, the flow coupling between the ERCOFTAC centrifugal impeller and the diffuser was conducted, and the steady and unsteady results were obtained and compared with the literature. And good consistency was observed by comparison. It shows that the algorithm is capable of forcasting the rotor-stator flow coupling. The algorithm can be used to forecast and investigate the centrifugal pump flows.