In aerospace applications, the Field Programmable Gate Array (FPGA) is attractive for its distinct advantages - simplicity and flexibility. But radiation-induced faults, especially Single Event Upsets (SEUs), may cause serious damage to SRAM-based FPGAs and even to the whole system. To restrain the consequences of SEUs and recover the system from radiation-induced faults, a hierarchical detection-mitigation-correction methodology based on XC4000 series FPGAs is introduced in this paper. The following techniques are included: fault identification and mitigation, soft-fault judgement and correction, hard-fault location and bypass. The effectiveness of our approach is proved through experiment and simulation. Such a detection-mitigation-correction methodology can cover almost all radiation-induced soft and hard faults and mitigate the effects of SEUs for general SRAM-based FPGAs without interrupting normal operations of the whole system