With the maturity of fast cut back（FCB）technology of large-scale thermal power units，it is now possible to use the FCB unit as the black-start power supply after a blackout.Planning the location of FCB units should take the engineering practice into account.The properties of the optimized placement scheme of FCB units are derived with the graph theory method.The successive property of the optimal placement scheme with known active point numbers is proved.Then the recursive method is presented for optimizing the placement scheme of FCB units.An economic index is then developed.Based on the calculating results of the recursive method，a placement scheme of FCB units meeting both safety and economic requirements can be obtained according to the economic index.Example analysis results show that the recursive method is more efficient and has a higher robustness than the conventional method.Meanwhile，with reference to the economic index，it can be seen that the calculation results can be used as a basis for black-start power supply planning.