This paper presents a fine-grain supply-voltage-control scheme for low-power FPGAs. The proposed supply-voltage-control scheme detects the critical path in real time with small overheads by exploiting features of asynchronous architectures. In an FPGA based on the proposed supply-voltage-control scheme, logic blocks on the sub-critical path are autonomously switched to a lower supply voltage to reduce the power consumption without system performance degradation. Moreover, in order to reduce the overheads of level shifters used at the power domain interface, a look-up-table without level shifters is employed. Because of the small overheads of the proposed supply-voltage-control scheme and the power domain interface, the granularity size of the power domain in the proposed FPGA is as fine as a single four-input logic block. The proposed FPGA is fabricated using the e-Shuttle 65 nm CMOS process. Correct operation of the proposed FPGA on the test chip is confirmed.