A theoretical investigation has been made to predict the flow pattern within a radial blade centrifugal pump. A mathematical model based on steady two-dimensional incompressible Navier-Stokes (N-S) equations has been developed. The real flow was modeled under these considerations. A computational-fluid-dynamic scheme was suggested using the primitive variables with artificial compressibility. The predictor-corrector method proposed by MacCormack was employed for its advantages of accuracy, less complexity, reasonable storage and convenient stability limit. A stability criterion was suggested and a fourth-order extrapolation smoothing term was used to limit the higher variations of the primitive variables. The use of this technique involved imaginary rows behind walls, and periodic boundaries at far upstream and downstream which adequately improved the convergence to the solution. Based on this model a computer program capable of predicting the flow pattern and pump characteristics inside the radial blade pump has been developed. The validity of the developed computer program, has been proven by comparing calculated and measured pump characteristic, which showed good agreement.