This paper presents a fast demodulation algorithm to determine fiber Bragg grating (FBG) from spectra acquired by low wavelength resolution spectrometers. A modified and improved Buneman frequency estimation algorithm is employed in tracking FBG wavelength and eliminating FBG wavelength discontinuities in real-time wavelength demodulation calculations. The FBG demodulation algorithm was tested using a 512-element detector array spectrometer with a 156 pm/element resolution. At a 2-kHz spectrum acquisition rate, the demodulation algorithm achieved a 0.048 pm Bragg wavelength resolution. The computational efficiency and robustness of the new algorithm was compared with a Gaussian FBG peak fitting method. Our method provides a real-time demodulation scheme to track FBG wavelength using low-resolution spectrometers or tunable lasers. It has the potential to significantly reduce the cost of FBG interrogation systems that are employed in high-sensitivity and high-speed sensing applications.