A novel fiber-optic sensor system is suggested in which fiber Bragg grating sensors are demodulated by a wavelength-sweeping fiber laser source and a spectrometer. The spectrometer consists of a diffraction grating and a 512-pixel photo-diode array. The reflected Bragg wavelength information is transformed into spatial intensity distribution on the photo-diode array. The peak locations linearly correspond to the Bragg wavelengths, regardless of the nonlinearities in the wavelength tuning mechanism of the fiber laser. The high power density of the fiber laser enables obtaining high signal-to-noise ratio outputs. The improved demodulation characteristics were experimentally demonstrated with a fiber Bragg grating sensor array with 5 gratings. The sensor outputs were in much more linear fashion compared with the conventional tunable band-pass filter demodulation. Also it showed advantages in signal processing, due to the high level of photo-diode array signals, over the broadband light source system, especially in measurement of fast varying dynamic physical quantities.