The centrifugal pump performance depends to great extent upon the flow pattern in the impeller passages. When the pump operates at small flow rates, the problem of circulation due to vortex formation in the impeller passages is found. A new method is introduced to control and reduce the size of generated vortices in the impeller passages. Slots are opened in the impeller vanes to allow fluid to flow from the pressure side to the suction side of the vane. The bleeding fluid could reduce the size of the vortices. It is found to depend mainly upon the length and the position of the slot. In the present work, the flow field is solved in the radial impeller passages using the stream function and the primitive variable approaches, to solve the flow equations. The flow pattern is used to compare the vortex size and the pump head for both cases with and without slotted impeller vanes at different slot sizes and at different positions. The slot position that produces the highest pump head, the slot length has been changed until the smallest vortex size is achieved. The numerical solution is introduced in a code program form, which is written in the Microsoft Visual C++ 6 language. Finally the optimum position and length of the slot is obtained at Rs/R2 = 0.4981, and with L /(R2-R1)= 0.2291. The model has been validated by comparison to a published experimental result of the same pump (for the same research program).