We report a resonance fiber Bragg sensor interrogation based on a Fourier domain mode-locking (FDML) laser. The FDML laser is constructed based on a conventional ring laser cavity configuration with fiber Fabry-Perot tunable filter (FFP-TF). There are two sensor parts which are composed with two FBGs inside the laser cavity. Each sensor part provides a separate laser cavity for the FDML laser. The resonance frequencies of the laser cavities are 46.687 kHz and 44.340 kHz, respectively. We applied a static and a dynamic strain on the FBG sensor system. The slope coefficients of the measured relative wavelength shift and relative time interval from the static strain are found to be $0.61pm/{mu}{epsilon}$ and $0.8ns/{mu}{epsilon}$, respectively.