Aiming at the problem that high density data results in challenge for data transmission and storage in fibber Bragg grating (FBG) sensing system, we propose a segmented adaptive sampling compressed sensing and improved orthogonal matching pursuit (SASCS-IOMP) algorithm. Firstly, we design the Gabor filter with specific parameters to extract frequency points of the upper sideband with the largest slope in the FBG spectral signal, and adaptively segment the FBG spectrum according to the coarse positioning of the FBG central wavelength achieved by the Hilbert transform. Then, we set different signal to noise ratio (SNR) thresholds in different segmented regions to reduce the overall compression ratio. To speed up algorithm speed, we design an adaptive step growth mechanism based on proportional-integral-derivative control algorithm in the process of adaptive sampling. Finally, we use IOMP algorithm to reconstruct the spectrum. The simulation result shows that the SASCS-IOMP algorithm can reduce the total number of observations in both the single-peak and multi-peak spectra. The reconstructed root mean square error is less than 0.7% within 3 dB bandwidth of FBG spectrum.