We propose an interrogation-system with automatic recognition and delay correction functions of fiber Bragg gratings (FBGs) by pulse modulation with a wavelength-swept laser. By pulse-modulating the light of a wavelength-swept laser, light with an arbitrary wavelength bandwidth can be extracted as the pulsed light. In the automatic recognition function of FBGs, the pulsed light is sequentially controlled to match the wavelength bandwidth of each FBG. This recognition method enables the selection and detection of a reflection signal from a single FBG. Therefore, reflection signals from multiple FBGs can be recognized individually. When multiple FBGs are installed at long distances, the reflection signal of each FBG is affected by the propagation time (delay). In the interrogation system with the wavelength-swept laser, the delay lowers the measurement accuracy. Therefore, a delay correction function using bidirectional sweeping of the wavelength-swept laser is used. The wavelength-swept laser using Fourier domain mode locking (FDML) is driven at a sweep frequency of 50.7 kHz with a sweep bandwidth of ∼60 nm. This study demonstrates that pulse-modulated FDML laser can automatically recognize reflection signals from multiple FBGs installed at arbitrary long distances. When the recognition process is complete, the interrogation system can perform real-time measurement with a time resolution of 9.9 µs, without being affected by delay that occurs when installing at a long distance.