Fault restoration on regional power grids is a multi-objective, multi-constrained and complex optimization problem. An analytical model based on subsystem-switch for on-line fault restoration is built. Based on the matrix elimination, the algorithm of searching recovery path is presented. Targeting at the recovery of the connection strength, design the restore strategy. Considering the overload of the line flow, bus bar voltages beyond limits, the number of switching operations and the network loss, the evaluation formula is built to select the optimal path. The method can carry out the on-line quick search of the optimal restoration path. The validity of the algorithm has been verified by practical cases of fault restoration.