Thermal power units with fast cut back（FCB）function can maintain the auxiliary power and keep islanded operation after the grid blackout.Thus they can be considered as black-start power sources for power system restoration.The steady-state behavior of FCB units during system restoration is analyzed and modeled.The unit start-up sequence is determined by developing an optimization mathematical model with a target of maximizing the total output power of generators and some unit constraints.Based on the physical essence of the optimization model，a modified area method is presented to speed up the calculation process.Then，taking the limited line charging-time into account，the unit start-up path is got by using the shortest path algorithm to correct the unit start-up sequence.The effectiveness of the model and method proposed is validated by simulations on the New England10-unit39-bus power system as well as a practical regional system.Simulation results show that thermal power units with FCB function are helpful to power system restoration.