We propose a real-time measurement system that prevents overlapping reflection signals in fiber Bragg gratings (FBGs). The system combines a wavelength-swept laser using Fourier domain mode-locking (FDML) and a buffer stage with three optical paths to obtain a high-speed measurement rate of 304.2 kHz. Systems using high-speed wavelength-swept lasers are affected by the propagation time (delay) of the optical fiber. The delay causes problems such as inaccurate measurements, difficulty in distinguishing FBG reflection signals, and overlapping FBG reflection signals. To prevent these problems, we introduce a method for pulse modulation of a wavelength-swept laser by a fiber switch. This method allows for correction of delays by extracting and identifying only the reflection signal of the FBG at a specific wavelength. By identifying the reflection signals of all FBGs, the overlapping signals can be determined. Accordingly, we devise a measurement method that uses a fiber switch to shade light in the wavelength region of one FBG with overlapping signals from the wavelength-swept light of the laser. This method suppresses overlapping and allows only the reflection signal of the other FBGs to be extracted and demodulated. The proposed system uses bidirectional forward and backward scans with the wavelength-swept laser, such that the shaded FBG signals can be demodulated with either scanning direction. We demonstrate that the system using a threebuffered FDML laser can simultaneously measure the strain or vibration of FBGs installed at arbitrary distances.