The inrush current is a highly asymmetric transient magnetizing current resulting from saturation of the core of the transformer caused by excessive growth of magnetic flux in one direction only. The suggested strategy to damp the inrush current is adding an inductor in parallel with the circuit breaker (C.B., which has a very low resistance when it is closed) at different values of the adding inductor to determine the suitable values of the inductor to damp the probable inrush current. This strategy differs from other strategies because the damping inductor is connected in parallel with the C.B. only at closing the C.B. for a few cycles, The damping inductor prevents the excessive growth for the flux in the core of the CT which lead to saturating the core of CT and then, prevents the excessive growth for the inrush current for specific situations of switching. Finally, the MATLAB program is used to simulate the suggesting strategy.