We develop a field-programmable gate array (FPGA)-based multichannel measurement system for sensing multiplexed fiber Bragg gratings (FBGs), using a high-speed wavelength-swept laser. The wavelength-swept laser, operated with Fourier-domain mode locking (FDML), exhibits a sweep frequency of 50.7 kHz and sweep band of ∼60 nm. A breakthrough in multichannel and real-time measurement is achieved by implementing an FPGA with unique parallel-processing circuits. This FPGA enables the implementation of a high-speed centroid-peakdetection circuit for FBG detection, which can be operated with a sampling frequency of 250 MHz. In multichannel measurement systems, the light propagating through each sensor path produces a delay, which reduces the measurement accuracy. This can be solved by implementing a delay-correction technique, which utilizes the time difference between two spectra obtained by a bidirectional scan of the FDML laser. The system is demonstrated to exhibit multichannel sensing and high measurement time resolution of 9.9 µs, without being affected by the delay.